What was found
CLEARED TO DEPART RUNWAY 7L AND FLY HEADING OF 080 TO 3000 FT MSL. AFTER TAKE, TURNED TO HEADING 080 AND ENGAGED AUTOPILOT WHILE IN THE CLIMB. IMMEDIATELY AFTER ENGAGING THE AUTOPILOT RED MASTER CAUTION FLASHED. FIRST OFFICER SAID IT WAS FOR AUTOPILOT TRIM LIGHT. CLEARED DIRECT TO 7000 FT MSL AND DIRECT TO TUSTI ON LAXX1 DEPARTURE. ATTEMPTED TO RE-ENGAGE AUTOPILOT AND RED MASTER CAUTION AND RED AUTOPILOT TRIM LIGHT ILLUMINATED AGAIN. REQUESTED VECTOR AND MAINTAIN 7000 FT MSL SO WE CAN RUN CHECKLISTS. CLEARED HEADING 210 AND TRIED TO RE-ENGAGE AUTOPILOT. NO SUCCESS. DECLARED EMERGENCY FOR AUTOPILOT FAILURE AND REQUESTED TO HEAD BACK TO LAX. REVIEWED FCS DIAGNOSTICS AND SAW NO ERRORS. FOUND THE FAILURE IN LRU DIAGNOSTIC HISTORY. PERFORMED THE TROUBLESHOOTING GUIDE FLOW CHART, WITH NO FAULTS. SWAPPED THE FCC CARDS WITH REFERENCE TO LEAR JET 60/60XR MM 31-40-01. MOVED P/N 822-0592-407 S/N 373 FROM SPOT 1 TO SPOT 2. MOVED P/N 822-0592-407 S/N 683 FROM SPOT 2 TO SPOT 1. PERFORMED AUTOPILOT FUNCTIONAL TEST. SYSTEM FAILED AT STEP 11(G). AGAIN PERFORMED THE TROUBLESHOOTING GUIDE FLOW CHART WHICH REVELED THE TRIM ACTUATOR TO BE SUSPECTED BAD. INSTALLED OVERHAULED PITCH TRIM ACTUATOR P/N: 622-5027-002 S/N: 1LW5P. REFERENCE 22-10-03. PERFORMED AUTOPILOT FUNCTIONAL TEST WITH REFERENCE TO LEAR JET 60/60XR MM 22-10-00.