A B757-200 WAS DISPATCHED WITH THE #1 ENG CORE OR FAN REVERSER COWLING UNLATCHED WHICH OPENED INFLT INCURRING DAMAGE TO THE COWLING; WING LEADING EDGE DEVICES AND THE L HORIZ STABILIZER.

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WORKING ON ACR ACFT; L ENG HAD OIL LEAK. OPENED ENG COWLINGS LOOKING FOR OIL LEAK. RECLOSED ENG COWLING TO BE RUN TO CHK FOR LEAK. REOPENED ENG COWLING FOR SECOND TIME FOR SECOND LOOK AND FOUND OUT THAT OIL LEAK WAS WITHIN LIMITS WITH MAINT CTL PER MAINT MANUAL. STARTED TO RECLOSE ENG COWLING; WHEN I HAD A MAINT CALL FROM CLEANING DEPT FOR SEAT BELT. I THEN WENT TO GET CLEANING DEPT A SEAT BELT. I THEN RETURNED; COMPLETED CLOSING OF ENG COWLING; BUT CANNOT REMEMBER IF THE CORE COWL WAS LATCHED CLOSE THEN. ACFT ENG LOOKED NORMAL DURING START WHEN DEPARTING. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE L ENG WAS OPENED TWICE FOR AN OIL LEAK PROB; BUT COULD NOT RECALL IF THE CORE COWLING WAS LATCHED PRIOR TO DEP. THE RPTR SAID THE ACFT TOOK OFF AND THE CORE COWLING OPENED INFLT; DAMAGING THE COWLING. WING LEADING EDGE DEVICES AND PIECES OF THE COWLING DAMAGED THE L HORIZ STABILIZER. THE RPTR STATED THE LATCHES SUCK UP INTO THE COWLING; AND THERE IS NO VISIBLE INDICATION THE COWLING IS NOT LATCHED.