The suspect, identified as Rhett Nelson of St. George, Utah, is also suspected in the fatal shooting of another man in central Los Angeles Monday evening, according to police.
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Deputy Joseph Solano, 50, was off-duty and in civilian clothes as he stopped at the Jack in the Box in Alhambra on Monday, while getting an oil change for his ill mother's car at a nearby Jiffy Lube.
Sheriff Villanueva discusses arrest of man in shooting of deputy in Alhambra
He was getting his food when a man approached and shot him in the head. Solano was listed in grave condition and remains on life support LAC+USC Medical Center as of Tuesday, according to Sheriff Alex Villanueva.
Solano worked as a custody deputy at the same hospital where he's being treated.
Officials say there appears to be no connection between Nelson and Solano and no obvious motive.
Solano was described as a dedicated family man. His father passed away a few months ago and he is now the sole provider and caregiver for his mother.
"He definitely is a kindhearted, generous person," Sheriff Alex Villanueva said. "Always willing to help others before himself. Has a bright smile, very positive individual. Everyone likes working with him, so we're all rooting for him to make a recovery."
Tuesday morning, Nelson apparently stopped at a church in Long Beach and called his father to say he had committed murder in Southern California, sheriff's officials said.
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His father called authorities in Long Beach, who were able to trace the number his father gave them to the church.
They found Nelson driving a short distance from the church, in the 2400 block of Granada Avenue in Long Beach, around 10:40 a.m. Tuesday and pulled him over. Sheriff's investigators were later able to connect him to the shooting and place him under arrest.
Nelson had previously been listed as a missing person out of Utah. In a social media posting, family members said he has a history of opioid use and had been missing since May 27.
Los Angeles Police chief Michel Moore says investigators are also connecting Nelson to the fatal shooting of a person in the 1900 block of 7th Street in central Los Angeles.
In that shooting, a car drove up to someone standing on the street. The driver had a brief exchange with the victim and opened fire. The person died at the scene and the vehicle fled. The suspect, clothing and vehicle description match those in the Alhambra shooting, Moore said.
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After the Alhambra shooting, a massive manhunt had been launched for the suspect seen in surveillance footage shooting the deputy at the restaurant, leaving him in critical condition.
"The shooting is on video," said Capt. Kent Wegener. "There doesn't appear to be an overt motive. There is no audio to the video, so we don't know if there were words exchanged."
RELATED: LASD sheriff's deputy shot at Alhambra Jack in the Box
LASD sheriff's deputy shot at Alhambra Jack in the Box
A $100,000 reward was offered for information leading to the arrest and conviction of the gunman who shot the deputy, but the suspect was found soon after.
Nelson was later booked and his bail was set at $2 million.
Anyone with information about the incident is encouraged to contact the Los Angeles County Sheriff's Department's Homicide Bureau at (323) 890-5500. If you wish to remain anonymous, call "LA Crime Stoppers" by dialing 800-222-TIPS (8477).