What was found
(CAN) REPORT FROM MAINTENANCE AND ENGINEERING MANAGER, THEN CONFIRMED WITH MFG TRAINING PILOT OPERATING THE ACFT, AFTER TAKEOFF WITH APU BLEEDS ON WHEN THE ACFT SWITCHED OVER TO ENGINE BLEEDS THE AFT PART OF THE CABIN FILLED UP WITH SMOKE AND CAUSED THE AFT LAVATORY SMOKE DETECTOR TO GO OFF AND CAUSE AN AFT LAVATORY SMOKE INDICATION ON THE EICAS. THERE WAS NO SMOKE IN THE FWD PART OF THE ACFT. SPEAKING WITH THE MFG PILOT, THIS LASTED FOR APPROXIMATELY 1 MINUTE BEFORE THE SMOKE DISSIPATED AND THE AFT LAVATORY SMOKE EICAS MESSAGE WENT AWAY. THERE WAS NO ACTUAL, OIL OR ELECTRICAL BURNING ODOR REPORTED. ON BOARD MECHANIC COMPLIED WITH SL 21-028 AND COULD NOT DUPLICATE THE FAULT. FAULT DID NOT OCCUR ON THE FIRST FLIGHT OF THE DAY BUT I WAS INFORMED BY MFG PILOT THAT THE APU BLEED WAS NOT USED ON THAT FLIGHT. ACFT HAS BEEN RETURNED TO SERVICE AFTER PERFORMING TROUBLESHOOTING AND NOT BEING ABLE TO DUPLICATE.