AN SF3 CAPT DESCRIBED AN RA HE HAD WITH A B757; BEING CTLED BY ANOTHER SECTOR; THAT DID NOT STOP AT ITS ASSIGNED ALT.

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WHILE CLBING ON MIA 5 DEP (WINCO TRANSITION) TO 8000 FT; RECEIVED REVISED CLRNC TO STOP CLB AT 6000 FT. UPON DOING SO; MIA DEP TOLD AN ACR B757 ON DSCNT TO FLL TO STOP DSCNT AT 7000 FT. FOR AN UNKNOWN REASON THE ACR PASSED THROUGH 7000 FT AND WAS APPROX 2 NM IN FRONT OF OUR ACFT AND DSNDING INTO US. TCASII ORDERED AN RA OF DSCNT OF AT LEAST 4000 FPM AND I ALSO SHARPLY TURNED R OFF THE SID. THE B757 WAS VISUALLY SIGHTED OFF MY L; STILL DSNDING AND MAKING A R TURN ALSO. I LEVELED OFF AT APPROX 4200 FT MSL ON A 90 DEG HDG; INSTEAD OF THE 322 DEG HDG OF THE TRANSITION. ATC WAS CONTACTED AND ADVISED OF THE RA CONFLICT AND I RETURNED TO THE DEP SID. I CONTACTED ATC IN MIA AFTER THE FLT AND SPOKE WITH A SUPVR WHO INFORMED ME THAT THE B757; FOR AN UNKNOWN REASON; CONTINUED DSCNT THROUGH HIS ASSIGNED 7000 FT AND EVEN SAID THAT HE HAD US IN SIGHT. ALSO; A SEPARATE APCH CTLR WAS TALKING TO THE B757 INITIALLY AND WAS NOT COORDINATING WITH MY CTLR UNTIL THE LAST MIN. AT THIS POINT; IT WAS TOO LATE AND EVASIVE ACTION WAS TAKEN. NO PAX OR FLT ATTENDANTS WERE INJURED AND THE FLT CONTINUED AS NORMAL.