ON APCH TO SJU ARPT; A B757 HAS AN NMAC WITH A TWIN CESSNA THAT TURNED ONTO FINAL IN FRONT OF THE FLT.

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OPERATING AN ACR X; B757-200 FROM JFK TO SJU. I SERVED AS FO AND FLEW THIS SEGMENT. UNEVENTFUL FLT UNTIL NEAR CONDO OM (FAF FOR ILS RWY 10). WE SEQUENCED BEHIND A FALCON JET. A TWIN CESSNA ON A R DOWNWIND AND THE LCL TWR CTLR HAD THE FOLLOWING EXCHANGE AS WE DSNDED ON THE GS INSIDE CONDO: TWIN CESSNA INQUIRED 'CONFIRM WE ARE #1 FOR THE ARPT.' TWR RESPONDED; 'ROGER TWIN CESSNA...; YOU ARE #1 BEHIND AN ACR Y.' TWIN CESSNA ANSWERED; 'OK; WE'LL KEEP IT IN CLOSE THEN.' THE CTLR'S NON-STANDARD PHRASEOLOGY AND TWIN CESSNA'S RESPONSE INSTANTLY HAD US LOOKING FOR A TFC CONFLICT; BUT BEFORE THIS AMBIGUITY COULD BE RESOLVED; THE FALCON PLT GOT ON THE FREQ TO RPT HE COULD NOT FIND THE TXWY TO EXIT THE RWY. AS AN INTENSIVE VISUAL SEARCH FOR THE TWIN ENSUED; IT BECAME CLR WE HAD SEVERAL PROBS. THOUGH VFR CONDITIONS PREVAILED; TFC WAS DIFFICULT TO ACQUIRE DUE TO BEING LOST IN THE LIGHTS OF SAN JUAN. AT 700-800 FT AGL WE SIMULTANEOUSLY ACQUIRED A VISUAL ON THE TFC; NOW ON A BASE LEG ON A PERFECT COLLISION COURSE. WE INITIATED A GAR AND RECEIVED INSTRUCTION FROM TWR TO GO AROUND. IRONICALLY; THE TWR GAVE THE GAR BECAUSE OF THE FALCON ON THE RWY AND NOT BECAUSE OF THE TWIN CESSNA CONFLICT. AT THIS POINT; TWR CTLR WAS UNAWARE OF THE TFC CONFLICT. WE ESTIMATE MISSING THE TWIN BY ZERO FT IN THE HORIZ PLANE AND 100-200 FT VERTLY. TCASII RA WAS INHIBITED IN THIS PHASE OF FLT.