ACR X DSCNT THROUGH OCCUPIED ALT HAD LTSS FROM ACR Y. SYS ERROR.

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I WAS CTLING ACR X IN THE ARR CORRIDOR ENRTE TO LAND AT FLL. ALSO IN THAT CORRIDOR WAS ACR Y LNDG MIA AT 7000. ACR X WAS AT 8000 AND REQUESTED A WBOUND HDG TO AVOID WX. THERE WAS WX EVERYWHERE COVERING MOST OF S FL; ESPECIALLY OVER FORT LAUDERDALE AND MIAMI AREAS. BOTH ACFT WERE DUE SBOUND AT THIS TIME; IN CLOSE PROX TO EACH OTHER SEPARATED BY ALT AT THIS TIME. THERE WAS MUCH COORD TO BE DONE DURING THIS TIME FRAME SINCE WHEN ACFT DEVIATE THEY PENETRATE OTHER SECTOR'S AIRSPACE. IT APPEARED TO ME THAT ACR X WAS 1/4 MI W OF THE PROP; SO I TURNED ACR X TO A WBOUND HDG AND DSNDED HIM TO 7000 SINCE HE WAS HEAD-ON WITH ANOTHER JET AT 6000. HE ASKED ME WHAT ALT HIS 2 O'CLOCK TFC WAS AT AND I TOLD HIM 6000. ABOUT 5 SECONDS LATER; HE SAID 'MY TFC IS AT 7000' AND DSNDED BELOW 7000. HE FILED AN NMAC. THE SUPVR IN CHARGE OF THE SATELLITE SECTOR INFORMED ME THAT THERE WAS PROBABLY A BEACON DISPLACEMENT OF UP TO 1 MI SINCE ACR X WAS ON THE FLL RADAR SYS AND ACR Y; LNDG MIA; WAS ON THE MIA BEACON SYS. I BELIEVE THAT THE ALPHANUMERIC DATA BLOCKS FLIP-FLOPPED TO OFFSET ONE FROM THE OTHER; THERE; I BELIEVED ACR X WAS W OF THE PROP; WHEN; IN FACT; HE MOST LIKELY WAS NOT. SOME NEW MODERNIZED ATC EQUIP COULD ALLEVIATE THIS FROM HAPPENING IN THE FUTURE. SUPPLEMENTAL INFO FROM ACN 206070: ACR X RADAR VECTOR BY MIA APCH FOR FLL. DSNDING ON A R DOWNWIND TO RWY 27 AT FLL AS WE PASSED APPROX 4500 FT MY COPLT AND A DISPATCHER ON OUR JUMP SEAT BOTH CRIED OUT AS AN ACFT APPEARED OUT OF THE CLOUDS IMMEDIATELY BENEATH US AND VERY CLOSE. I HAD ABOUT 1 MIN EARLIER TURNED OUR TCASII FROM THE TA/RA MODE TO THE TA MODE TO AVOID NUISANCE ALERTS NEAR THE ARPT. THERE WAS AN ACFT ABOUT 1500 FT ABOVE US ON THE TCASII SCREEN COVERING THE TCASII SYMBOL OF THE ACFT THAT WENT BENEATH US; AN ACR Y. ON THE GND; I SPOKE ON THE PHONE WITH AREA MGR -- MIA TWR; AND HE EXPLAINED THE SCENARIO TO ME AND STATED IT APPEARED THAT AN 'OPERROR' HAD OCCURRED. THERE WERE TSTM CELLS ALL AROUND AND ACFT WERE BEING VECTORED TO STAY CLR. WE WERE BEING VECTORED BY SAME CTLR AND IMMEDIATELY THEREAFTER; ANOTHER CTLR TOOK OVER. THE ACR Y NOTICED US AT ABOUT THE SAME TIME WE NOTICED THEM. THE DISPATCHER STATED IT APPEARED TO HIM THAT THE ACR Y ACFT WAS IN A STEEP R BANK AT THE TIME.