Peter F. Morgan, the prince George's police man who was fired for shooting an unarmed shoplifting suspect, cannot be reinstated by County Executive Lawrence J Hogan under the current county charter.

Morgan became a symbol of Hogan's efforts to woo both police officers and the county's law and order voters during Hogan's campaign for county exective. He never publicly promised to reinstate Morgan-who shot the shoplifting suspect in the back as he fled from the Seat Pleasant police station - but often said Morgan had been made a "scapegoat," and that Hogan would "take care". of him.

So, shortly after his election, he asked the county attorney's office to investigate the legility of rehiring Morgan.

On Nov. 27, howerve, Hogan was told in a confidential memo that Morgan could not be rehired unless he wins a reversal of his dismissal in court.

Morgan was fired on June 21 after a three-man police trial board found him guilty of using deadly force improperly.

Morgan's firing became a cause celebre among rank-and-file police officers who attacked both Police Chief John W. Rhoads and County Executive Winifield M. Kelly for the firing. The police union, the Fraternal Order of Police, campaigned heavily for Hogan, as did Morgan, Morgan said after Hogan's victory that he was "confident," he would be back on the force, "early in 1979." Hogan would not comment then on whether he wanted to rehire Morgan and again refused comment yesterday.

Police sources said Hogan had asked for the legal memo because he had promised them that Morgan "would be taken care of," if Hogan were elected.

Morgan has appealed his firing and if he wins his case in circuit court he will be reinstated. But if the court rules against Morgan the only way he could return to a county job would be in an exempt position in the county government. There are only about 20 positions that are exempt from county merit regulations. They include department heads and top aides to the county executive.

In the memo, headed, "Re: Reappointment of Peter F Morgan," Barr wrote, "if the County prevails, it is our opioion that Mr. Morgan is not eligible for reinstatement in the police force, any position in the employ of Prince George's County, Maryland, or the Sheriff's County, Maryland, or the Sheiff's Department of Prince George's County, Maryland.

"Inded, it is our opion," Barr wrote later, "that the express prohibition contained in Section 16-148(a)(8) act as a permanent bar to prohibit the appointment of Mr. Morgan to any position in the classified service of Prince George's County, Maryland."

Morgan, 23, currently is working at a local car dealership selling auto parts. His shooting of William Ray, 23, of Northeast Washington, was followed four weeks later by another shotting of a black suspect by a white policeman. The two incidents touched off anger within the black community toward the police force.

Hogan labeled Morgan's firing as "politically motivated," during the campaign, saying Kelly had made Morgan "a scapegoat."

The Morgan case was one of the major reasons that the police backed Hogan. The county executive has insisted all along that he made no commitments about Morgan to the police. Sources said yesterday, however, that the study of Morgan's rehiring, "was one of the first things," Hogan did after being elected.

Rhoads has publicly defended the firing on numerous occasions, saying it was his, not Kelly's decision. "Being second-guessed is part of my job," Rhoads said yesterday. "I think as people, Hogan included, get to know the case better, they'll understand why I did what I did.

"But I think I did the right thing. If he (Hogan) disagrees with me I don't consider that a judgement of my overall performance."