What was found
ACFT STALL WARNING & STICK SHAKER OCCURRED AT FL390. CREW TOOK EVASIVE ACTION INITIATING A DESCENT. STICK SHAKER CONTINUED FOR SOME TIME BEFORE STOPPING. CREW REPORTED THAT THE STALL WARNING OCCURRED AT FL390 & AGAIN AT FL340. CAPTAIN EXPRESSED CONCERN THAT SINCE THE AFT CARGO DOOR INDICATOR WAS DEFERRED THEY THOUGHT MAYBE THE DOOR HAD OPENED IN FLIGHT. DECLARED AN EMERGENCY. PRESSURIZATION HAD NOT BEEN LOST. FLT DIVERTED & LANDED WITHOUT FURTHER INCIDENT.. FOUND NR 1 LT AOA SENSOR CONNECTOR TO BE AT FAULT. REPLACED CONNECTOR IAW STANDARD PRACTICE M/M.