A VFR LTT; UNDER RADAR SURVEILLANCE; HAD AN NMAC WITH AN IFR LGT.

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40 NM NW OF ISP; WE STARTED OUR DSCNT INTO ISP. MY FO WAS FLYING. AFTER WE WERE HANDED OFF TO NEW YORK TRACON (FREQ 126.80) WE TOLD HIM THAT WE WERE DSNDING THROUGH (12000- 11000) AND HE SAID 'ROGER.' ABOUT 1 MIN LATER; I CAUGHT SIGHT OF AN ACFT AT OUR 2 O'CLOCK POS MOVING L ACROSS OUR 12 O'CLOCK POS. I CALLED TFC TO MY FO WHO IMMEDIATELY BANKED THE ACFT R AND WE PASSED WITHIN 300-500 FT BEHIND THE ACR LGT. WE PASSED RIGHT THROUGH THE LGT'S WAKE TURB. AFTER WE PASSED EACH OTHER; THE CTLR CALLED US AND SAID 'YOU HAVE TFC; ACR LGT; PASSING OFF YOUR L SIDE.' I REPLIED 'ROGER; WE MADE A TURN TO AVOID HIM.' THIS WAS HIS ONLY COM WITH US CONCERNING THE LGT TFC; AND AS FAR AS I KNOW; NO COM WAS MADE WITH LGT. IF WE HAD NOT BEEN MAINTAINING VFR AWARENESS ON OUR FLT; WE WOULD HAVE NOT SEEN THE LGT AND A MAJOR ACCIDENT MAY HAVE HAPPENED. AFTER LNDG ISP; I CALLED THE NEW YORK TRACON AND RPTED THE OCCURRENCE. I'M NOT SURE WHAT HAPPENED IN THAT RADAR ROOM; BUT I KNOW IT WAS MUCH TOO CLOSE IN THE AIR. AS A MATTER OF FACT; THAT IS EXACTLY WHAT THE LGT PLT SAID TO THE CTLR AFTER WE PASSED.