Reports by D.C. police of a promising lead in the shooting death of a popular Northeast Washington deli owner in June has renewed the family’s hope that the killer will soon be found, but it also has evoked a flood of painful memories.

The victim’s son, Peter D. Lim, said relatives have been concentrating on trying to sell the shuttered shop on H Street. He said detectives told him two weeks ago that they linked a man to the crime scene through DNA.

“We haven’t had a chance to deal with this whole thing emotionally,” he said of his mother’s death. “Now that it’s back in the news, it’s painful. It’s reopened the wounds and made it fresh again. But I think any progress is good. We’re hopeful.”

Hae Soon Lim, 64, was found fatally shot inside Grace Deli, at Seventh and H streets NE, on the morning of June 14. Neighbors and customers knew her as June.

Newly filed court documents say she was shot once in the back of the neck while standing behind her counter.

A police affidavit seeking a search warrant, filed in D.C. Superior Court last week, says that the deli’s cash drawer had been rifled and that an empty gun holster was found inches from Lim’s body.

A forensics technician with the D.C. police crime lab swabbed the holster for DNA, the affidavit says, and the results were submitted to a national database. The existence of the affidavit was first reported by Washington’s Fox 5 (WTTG-TV).

Police said that on Aug. 7, the DNA database matched the evidence from the discarded holster to a 46-year-old man, a convicted criminal in Virginia who was wanted on an alleged parole violation. Details of that case could not be ascertained.

D.C. police and members of the U.S. Marshals Service arrested the man Aug. 23 in an apartment in the 1200 block of M Street NW, where the affidavit says he had been living since May.

The Washington Post is not naming the man because he has not been charged in Lim’s death. Police said in court documents that the man is being held in the D.C. jail. Police declined to comment on the latest developments.

Police used the DNA match to obtain a search warrant for the M Street apartment, telling a judge that “there is probable cause to believe that inside the residence . . . may be secreted firearms, holsters, ammunition, photographs, diagrams and firearms manuals.”

But court documents show that police found nothing pertaining to the investigation. The affidavit says the man declined to talk with homicide detectives and asked for an attorney.

The victim’s son, Lim, who lives in Maryland, said detectives told him that the DNA link is insufficient to bring charges.

“We think this is a step in the right direction,” Lim said of the new developments. “I know this is the strongest link to anything they’ve had thus far. But I’m not really sure where they go from here.”

Jennifer Jenkins contributed to this report.