What was found
FLT#2536, STI-JFK. (AIRCRAFT PERFORMED AN AIR TURN BACK TO STI) 'UPON PASSING 10K FEET THE AFT LAVATORY F SMOKE DETECTOR TURNED ON IN THE BACK OF THE PLANE (NOT IN THE COCKPIT). IIT CAME ON THEN WENT OFF THE SMOKE DETECTOR CAME ON SHORTLY AFTER THE FIRST INDICATION WITH ASSOCIATED ELECTRICAL BURNING SMELL IN THE AFT; PERFORMED INSPECTION OF ELECTRICAL BURNING SMELL IAW TSM 24-00-00-810-823-A NO ODOR DETECTED. PERFORMED DUAL ENG RUN IAW AMM 71-00-00 ALL OPS CHK GOOD. VERIFIED ALL LAV SMOKE INDICATIONS OPERATING NORMALLY IAW AMM 24-93-00. A/C OK FOR CONT SVC.'