A third person was also in custody in connection with the May 17 murder, but charges have not yet been filed against that individual.
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One of the suspects under arrest is also accused of shooting and wounding another homeless person only days later.
The Los Angeles Police Department says Rubi Aguiano-Salazar, 37, was arrested for the murder of 69-year-old Gerold Lipeles.
On May 17, Lipeles was shot near the McDonald's on West Century Boulevard, police said. Investigators said he was asleep outside the restaurant when a woman walked up and shot him in the head.
Lipeles was described as a military veteran and double amputee.
When police developed information that led them to Salazar, she was already in custody for another shooting.
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The LAPD alleges Salazar shot a homeless woman in the back at a bus stop in South LA on May 21, only four days after Lipeles was killed.
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Salazar approached Stella Polly - a 67-year-old woman who was also experiencing homelessness - at a bus stop in front of 1606 West Manchester Avenue in South L.A., police say.
"After the suspect initiated conversation, Stella Polly walked away," an LAPD statement says. "The female suspect shot her in the back as she walked away."
Two other people have also been arrested in connection to Lipeles' death.
Police said 34-year-old Raymundo Hernandez and 32-year-old Blas Canche were also involved in the incident.
On Thursday, the Los Angeles County District Attorney's Office said murder charges have been filed against Salazar and Hernandez. Canche's involvement is still under investigation.
For the two incidents, Salazar is facing one count of murder, one count of attempted murder and two counts of possession of a firearm by a felon.
Hernandez is facing one count of murder.
"The murder of this victim - who was unhoused and a double amputee asleep in his wheelchair - is disturbingly brutal and callous," District Attorney George Gascón said. "I thank members of my Community Violence Reduction Division for their work in this case. We will hold those responsible accountable for this unthinkable crime."
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A motive for the shooting remains unknown.
Anyone with information is urged to contact police.