NMAC BETWEEN ACR-WDB DEPARING AND GA-SMA IN ATA.

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I WAS SERVING AS F/O ON THIS FLT. THE CAPT WAS AT THE CTLS. WE TOOK OFF RWY 17 AT SDQ AND COMMENCED A LEFT TURN TO JOIN W 4 CLBING TO FL280 AS CLRED. TWR SWITCHED THE FLT TO SANTO DOMINGO CTL ABOUT 1 MIN AFTER DEP; WHILE CLBING THROUGH 1500' AGL STILL IN A LEFT TURN. AS THE CAPT BEGAN HIS ROLL OUT HDG; APPROX 350 DEGS MAG; I SAW AN SMA; 10 O'CLOCK; ABOUT 100' ABOVE OUR ALT AND 400-500' HORIZ HDG APPROX 090 DEGS. I BROUGHT THE TFC TO THE ATTN OF THE CAPT WHO SPOTTED THE SMA ABOUT 9 O'CLOCK; APPROX 300-400' HORIZ AND SAME ALT. THE CAPT CONTINUED THE CLB AND ROLL OUT AND THE SMA PASSED BEHIND AND BELOW OUR ACFT. NO EVASIVE ACTION WAS TAKEN MAINLY FOR LACK OF TIME. THE SMA WAS IN SIGHT FOR A TOTAL OF 2-3 SECS. AFTER CHKING IN WITH SANTO DOMINGO CTL AND ASKING ABOUT THE SMA; WE WERE TOLD IT WAS NOT UNDER THEIR CTL. WE SWITCHED BACK TO LAS AMERICAS TWR QUESTIONING THE TFC. TWR TOLD US THAT THEY HAD ADVISED THE SMA THAT WE WERE DEPARTING AND THAT THE SMA SAID THEY HAD US IN SIGHT. WE WERE NEVER ADVISED OF THE PRESENCE OF THE TFC PRIOR TO OUR TKOF. RECOMMEND TWR NOT SWITCH US TO SANTO DOMINGO CTL WITHIN THEIR ARPT CTL AREA WHILE THERE IS TFC WITHIN THEIR AREA WHICH MAY CONFLICT. SUPPLEMENTAL INFO FROM ACN 88393: I BELIEVE THAT COM BTWN SDQ TWR AND THE SMA WAS IN SPANISH.