Moye had pulled over a pickup truck and was doing paperwork to impound it when the driver, who was outside the vehicle, reached in, grabbed a rifle and fatally wounded the officer.
Moye graduated from the CHP Academy in March 2017 and was assigned to the Riverside area.
The shooter opened fire shortly after 5:30 p.m. after a CHP officer pulled over a white GMC pickup truck and made a decision to impound it.
34, is survived by his wife Sara, both parents, his stepfather, two sisters and two brothers, and a large extended family, according to officials.
Late Monday night, KABC-TV reported that his father had identified the gunman as Aaron Luther, 49, of neighboring Beaumont. Their first encounter with each other happened when Moye was training to be a motor officer.
Other officers arrived and started shooting, Parker said, eventually hitting and killing the suspect.
The Highway Patrol officer and the suspect were rushed to nearby hospitals and declared dead after the shootout, police said.
"Officer Moye embodies everything that the California Highway Patrol stands for, with the professionalism, dedication and service to the public", Inland Division Chief Bill Dance said.
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Authorities said it was unclear what prompted Moye to stop the truck or for the driver to open fire.
"I am devastated by the tragedy that unfolded earlier in Riverside", CHP Commissioner Warren Stanley wrote on Twitter.
"I think he just, whatever else was going on with his domestic situations and his pain, I think he just thought he didn't have much to live for, and I think this might have been suicide by the police", Luther told KTLA5 from his home.
"It's hard, I love him", Luther said in an exclusive interview with ABC7. Newsom, who took office in January, said he's already been to "too many" funerals of officers killed in the line of duty. "In fact, I said a prayer for the policeman before I did for my son". Newsom's office also confirmed that Capitol flags will be flown at half-staff.
"I'm devastated", he said.
Luther told ABC7 his son had served 10 years in prison for attempted murder and was released more than a decade ago but recently suffered from depression and a knee injury. "I just can't believe it".
"She said she heard "pop, pop, pop". gunfire, and then a bullet went through the windshield of her auto", Luther said of his son's wife. "That's all he talked about", she told station. Dozens of rounds were fired, local media said, and motorists stopped in traffic fled their vehicles and ran for cover, media reports said.