A man who was already serving time in state prison when he was charged with the 1983 killing of a single mother in Los Angeles is expected to be sentenced in October to life behind bars without the chance of parole.

A downtown Los Angeles jury deliberated about 45 minutes Wednesday before convicting Teddy Jerome Young, now 63, of first-degree murder for the January 1983 shotgun slaying of 37-year-old Alice Faye Chatman.

Jurors also found true the special circumstance allegations of murder during the commission of a kidnapping and murder during the commission of a rape, along with an allegation that he personally used a shotgun during the crime.

Sentencing was scheduled for Oct. 1 before Los Angeles County Superior Court Judge Eleanor J. Hunter.

Los Angeles police had said Young — who was serving a 62-year-to-life sentence — was linked to DNA from a sexual assault kit collected from the victim after testing in 2014 and 2016.

In her closing argument Tuesday, Deputy District Attorney Negin Mostadim told jurors that the victim was an “easy target” and vulnerable as she walked to a bus stop on her way to work and that Young targeted her because he wanted her purse.

The prosecutor alleged that the defendant — who lived within a block of the victim — wasn’t able to easily get her purse away from her and took her to a house that he knew was abandoned, where he raped her and then shot her in the back. Mostadim said Young killed her because he didn’t want her to be able to leave and tell people what had happened to her.

“He didn’t need to kill her. He could have left her there,” the prosecutor said.

Defense attorney Glen Kiyohara countered that the crux of the case was identification.

“Who committed this crime? Who killed Ms. Chatman?” he asked jurors.

Young’s attorney said the DNA sample from the sexual assault kit was a “low-level DNA sample” and a “degraded DNA sample,” and questioned what had happened to it between 1983 and 2014. He also asked jurors to question whether it really showed Young’s DNA profile.

“Don’t just blindly take these results … Simply put, the DNA evidence in this case is based upon a false assumption … that there was only one donor,” he said. “There are no eyewitnesses, there’s no video.”

The prosecutor said in her rebuttal argument that the defense was “trying to convince you that it’s not him,” and maintained that Young’s DNA was detected in semen from the DNA sample “because he raped her.”

The deputy district attorney told jurors that for 40 years the defendant has not been ”held accountable,” saying “that stops now.”

Police said shortly after the case was filed that the victim was the single mother of a 13-year-old son and worked full-time to try to provide a better life for him. They described Young as having a “long criminal history” that included arrests for a series of robberies — most recently in 1997 in Riverside.