SAN DIEGO — A 30-year-old man accused of fatally shooting an off- duty sheriff's deputy in Los Angeles County is being investigated as a possible suspect in four San Diego County armed robberies and one attempted heist, police said Wednesday.

Rhett Nelson, of St. George, Utah, was arrested Tuesday in connection with the Monday afternoon shooting of Los Angeles County sheriff's Deputy Joseph Gilbert Solano. Solano, 50, who was off-duty, was shot in the head in an apparently random attack inside a Jack in the Box eatery in Alhambra.

Solano died Wednesday afternoon.

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Nelson is also suspected in a fatal shooting in downtown Los Angeles that occurred about 4:50 p.m. Monday, roughly one hour before Solano was shot.

Los Angeles County sheriff's officials on Wednesday morning released a mugshot of Nelson, saying they suspect he may have been involved in other crimes and encouraging anyone who may have been victimized by him to come forward.

San Diego Robbery Series

According to San Diego police, Nelson is being investigated in connection with five crimes that occurred over a three-day period in San Diego, Lemon Grove and Carlsbad. Nelson is a possible suspect in:

-- an 11 p.m. Friday armed robbery of a 7-Eleven store at 4205 Voltaire St. in San Diego;

-- an 11:55 p.m. Friday armed robbery at a 7-Eleven at 3185 Midway Drive in San Diego;

-- a 6:10 p.m. Saturday armed robbery of a 7-Eleven at 7607 Broadway in Lemon Grove;

-- a 10:45 p.m. Saturday attempted armed robbery of a 7-Eleven at 1702 Gateway Drive in San Diego; and

-- a 2:25 a.m. Sunday armed robbery of a Circle K store at 7602 El Camino Real in Carlsbad.

In all four successful armed robberies, the culprit made off with an undisclosed amount of cash. A handgun was brandished in all of the crimes, police said.

Authorities in San Diego would not release surveillance video.

The San Diego Police Department, Carlsbad Police Department and San Diego County Sheriff's Department have all been in contact with authorities in Los Angeles County to discuss Nelson's possible involvement in the crimes.

Nelson is being held without bail in Los Angeles County and could appear in court as early as Thursday.