LAX to San Diego flights depart from the "Eagles Nest". That is a remote terminal assessible with an airside bus.

If Dad is flying F or J, he will be able to go through AA's Priority Access TSA line in T4. He would drop his checked luggage at the recheck area just past the Customs check (very easy), then emerge from Customs in the Arrivals hall.

Next, walk landside to the adjacent AA T4, and proceed to the far end, where the Priority Access check-in area is, assuming F or J or elite status. If he needs a bp, he can get it there, or just go up the short escalator to the mezzanine and checkpoints.

The TSA Pre-Check and Priority Access people form two lines, but go through the same doorway. I assume Dad is not Pre-Check eligible, so with PA he should join the right-hand line. There are uniformed employees and signage to help.

If Dad does not have Priority Access, then he would go through the TSA checkpoint in the middle of the terminal.

Either way, he will emerge from TSA at the beginning of the T4 concourse departures level. He should walk towards the end of the concourse looking for what used to be called "Gate 44" but is now "Terminal Transfer". That is the place where he gets on an airside bus to the Eagles Nest. There is ample signage directing the passenger. He will go down a short escalator, the follow the signs.

What used to be called Gate 44 is not an airplane jetbridge gate, but just a bus pick up and drop off point, like FCC in LHR. Eagles Nest gates used to be numbered 44A, 44B, etc, but they were changed recently to 60A, 60B, etc. Once Dad arrives at the Eagles Nest, he should look at a monitor to determine which gate is his.

Having said all that, Dad should double-check his gate while still in T4, on the off chance the flight leaves from T4 or T6 and not the Eagles Nest. If the flight leaves from T6, he would still get the airside bus.

I would always prefer going through TSA in T4 instead of TBIT, even without Priority Access.

Edited: Thanks to IceTrojans correction, I wanted to make it clear that "Gate 44" is now signed as "Terminal Transfer".