The morning after the Nov. 22, 1963, assassination of President John F. Kennedy, his successor in the White House, Lyndon B. Johnson, was told by FBI Director J. Edgar Hoover that the bureau had "the tape and the photograph" of a man who "claimed" to be Lee Harvey Oswald visiting the Soviet Embassy in Mexico City less than two months before the murder.

"That's one angle that's very confusing," Hoover said. "That picture and the tape do not correspond to this man's {Oswald's} voice, nor to his appearance. In other words, it appears that there is a second person who was at the Soviet Embassy down there."

The specter of a "false Oswald" -- someone who may have helped the real Oswald or manipulated him -- is one of many suspected conspiracies that have haunted the assassination for three decades. Hoover's remarks, recorded by LBJ's secretary and just cleared for public release this month by the National Archives, illustrate why those suspicions will never die.

The tape Hoover mentioned was of a telephone call to the Soviet Embassy in Mexico City on the morning of Oct. 1, 1963, that was surreptitiously recorded by a CIA-run covert operation. In the call, a man identified himself as Lee Oswald and asked whether information had been received about a visa he was seeking to travel to the Soviet Union.

The photograph in question was taken by another secret CIA surveillance operation that took photos of people entering and leaving the Soviet Embassy in Mexico City. The man in this particular picture was photographed on Oct. 1, 1963, again three days later, and finally, at the Cuban Consulate, on Oct. 15.

The tape of Oswald's call has never been made public. The CIA has always insisted that while a transcript exists, the tape was routinely destroyed before the Kennedy assassination.

However, two staff lawyers for the Warren Commission say that CIA personnel in Mexico City played tapes for them of more than one conversation in the spring of 1964 and told them it was Oswald who was speaking.

No photograph of Oswald has ever come to light. The CIA station in Mexico City picked out someone else who visited the Soviet Embassy Oct. 1, thinking it may have been Oswald. Beginning the day after Hoover's statement, the CIA has always denied a photo of the real Oswald exists.

But House Assassinations Committee investigators concluded years later that the CIA's photo surveillance operations in Mexico City "probably obtained a photograph of Lee Harvey Oswald entering either or both the Soviet and Cuban consulates."

Such disputes help explain why the Kennedy assassination continues to cause controversy, and why eight out of every 10 Americans polled think there was a coverup to keep the public from learning the truth. Most of them -- three out of every four -- believe "others were involved," according to a CBS News/New York Times poll last month.

Hoover's conversation with Johnson began at 9:55 a.m. on Nov. 23, 1963, LBJ's first full day as president. Hoover's main purpose in calling was to bring the new president up to date on the overnight findings of the widespread FBI investigation. Although much progress had been made, Hoover told Johnson that morning: "The case {against Oswald}, as it now stands, isn't strong enough to be able to get a conviction."

Johnson, who suspected a conspiracy himself, wanted to know if the FBI had "established any more about the visit to the Soviet Embassy in Mexico in September."

"No," Hoover told him, explaining "that's one angle that's very confusing." But did the FBI director know what he was talking about that morning, less than 24 hours after the shooting? Here are some of the pieces that make up the puzzle:

CIA officials in Mexico City instantly recognized Oswald's name when he was arrested in Dallas on the afternoon of Nov. 22, 1963. But they did not know what he looked like. They recorded a call he made to the Soviet Embassy on Oct. 1 during which he mentioned a visit he had made to the embassy Sept. 28. On Oct. 9 the CIA officials asked Washington for a picture of the ex-Marine, one they could compare with photos they took of visitors to the two compounds on the days in question. (It turned out that they also had recorded other phone calls about visits Oswald made to the Soviet Embassy and the Cuban Consulate on Sept. 27 and 28.)

The photo request was forwarded to the Navy, but the Navy failed to respond until a full day after Kennedy was killed. The Office of Naval Intelligence belatedly mailed Marine Corps mug shots of Oswald to Mexico City in an envelope postmarked Nov. 23.

As soon as Oswald's name was broadcast on Nov. 22, CIA Mexico City station chief Winfield Scott cabled headquarters to remind them that on Oct. 9, he had informed them of Oswald's phone call to the Soviet Embassy. Scott again asked for a picture of Oswald so they could compare it to "all recent photo coverage." He also said he was sending Washington "copies of only visitor to Soviet Embassy Oct. 1 who could be identical with Oswald."

At the same time, the CIA station gave a set of those photos to their FBI counterparts in Mexico City. Some copies were flown to the Dallas FBI office and others to FBI headquarters in Washington, apparently at the urging of U.S. Ambassador to Mexico Thomas Mann. By Hoover's account, the dispatch also included a tape that purported to be of Oswald's voice.

As Hoover observed, the photos were clearly not of Oswald, but they were to cause a big problem early in the investigation. FBI agents showed them to Marguerite Oswald, Lee's mother, on the night of Nov. 23. She did not recognize the man, but as soon as Jack Ruby's picture showed up in the papers on Nov. 25 as Oswald's killer, she began claiming that the FBI had shown her Ruby's photo before he shot her son.

That was just the beginning of rumors about the burly "mystery man" whom the CIA for years said it was unable to identify. According to a recently released 1978 study by the House Assassinations Committee staff, one source named the man as Yuriy Moskalev, a KGB officer in Mexico City.

Retired KGB officer Oleg Nechiporenko, in his new book, "Passport to Assassination," identifies the man in the photo as "a former American serviceman, discharged for reasons of health." Nechiporenko, who served in Mexico City, goes on to say he talked to the man who visited the embassy several times.

A House committee staff member interviewed the CIA analyst in Mexico City who selected the mystery man photos. She told him she had no photos from Sept. 28, the day Oswald was known to have visited the Soviet Embassy, and so looked through those on Oct. 1 and picked out the only one who might have been an American.

When Oswald's real picture appeared in the Mexican press the day after the assassination, the CIA station told headquarters that it had rechecked "photos of all visitors to the Cuban Embassy" as well as the Soviet Embassy and found "no evidence {of} Oswald visit."

Committee investigators suspected, however, that the CIA, despite its protestations, must have photographed the real Oswald on at least one of his five visits to the Soviet Embassy and the Cuban Consulate. They concluded such a photo probably had been taken because some CIA personnel in Mexico City told them they had seen one, because CIA records indicated that photographic surveillance of the Cuban Consulate began on Sept. 27, a weekday when Oswald was there, and because of a 1970 manuscript left behind by station chief Win Scott when he died.

In it, Scott wrote that "persons watching these embassies photographed Oswald as he entered and left each one; and clocked the time he spent on each visit." Committee investigators said longtime CIA counterintelligence chief James Jesus Angleton testified in a deposition "that he had in fact cleaned out Win Scott's safe {after Scott's death}, but that he had not found any photographs. . . . "

Asked about the CIA's "possible withholding of photographic materials," the CIA told the committee there was no photographic coverage of the entrance to the Cuban Consulate on Sept. 27, 1963. The CIA supplied the committee with some of the photos it took outside the embassies during that period, but did not comply with a request for what investigators called "the most relevant" coverage: by the pulse camera that was trained on the entrance to the Cuban Consulate and by a late-shift operation aimed at the Soviet compound.

The committee itself said in its final report in 1979 that it was "unable to determine whether the CIA did in fact come into possession of a photograph of Oswald" during his visits to the embassies.

G. Robert Blakey, a Notre Dame law professor who was the committee's chief counsel, says he now believes the CIA did photograph Oswald and withheld it because "I think there are two people in it." There could be a perfectly innocent explanation for that, he says, but it would have posed a large problem for investigators.

A similar dispute has dogged the Oswald tape. On Nov. 23, 1963, CIA headquarters cabled its Mexico City station to send full transcripts of Oswald's conversations and "original tapes, if available," as soon as possible by special courier.

That same day, Nov. 23, FBI headquarters told the Secret Service that FBI agents who had talked to Oswald "have listened to a recording" purported to be of Oswald's voice and were of the opinion that it was not. Hoover gave the same report to President Johnson.

The next day, the CIA station in Mexico told CIA headquarters it was unable to obtain any tape of Oswald's voice. "Regret complete recheck shows tapes for this period already erased," the cable said. On Nov. 25, 1963, the Dallas FBI office told Hoover that "{t}here appears to be some confusion in that no tapes were taken to Dallas . . . {o}nly typewritten {reports were} supplied."

In April 1964, Warren Commission assistant counsels William T. Coleman Jr. and W. David Slawson, who were responsible for investigating any foreign involvement in the assassination, flew to Mexico City to look into Oswald's activities.

As part of their inquiry, CIA station chief Scott allowed them to listen to tapes of at least two Oswald conversations, Coleman and Slawson said in recent interviews. "The reproduction was not perfect," Coleman said, but with a written transcript the CIA provided him, "I picked up most of the words."

Slawson agreed the tapes were of very low quality, but said he had no reason to suspect it was not Oswald's voice. He said the tapes fit in perfectly with other accounts of Oswald's trip to Mexico. Coleman and Slawson said they were not aware at the time that the CIA had denied the existence of the tapes.

Why would these be hidden? There have been suggestions that they may have contained more detail than has been disclosed, such as Oswald asking for financial assistance. Another conjecture is that Hoover was right: the voice might not have been Oswald's.

The problem with the Kennedy assassination, Blakey said in a recent interview, lies in disputes such as this. "When you come to it and you look at it, it's like a Rorschach test. It tells you more about the person who looks at it than what's on the ink blot."

Researcher Ann Eisele and news aide Estella Mendoza contributed to this report.