What was found
AFT LAV SMOKE ALARM SET OFF FOLLOWING TAKEOFF AND DURING CLIMB. F/A SMELLED SMOKE AND VERIFIED NO FIRE. RETURNED TO JFK, SMOKE ALARM RESET ITSELF AND F/A STATED SMOKE ODOR DISAPPEARED. INSPECTED LAVS, AFT GALLEY, TAIL COMP, FOUND NO ODOR. VISUAL CHECK NORMAL. FOUND APU INLET SATURATED WITH OIL. RAN ENGS AND PACKS NO ODOR AND NO SMOKE. REPLACED COALESCER BAGS. CLEANED APU INLET AND PERFORMED DUCT BURNOUT.