LESS THAN STANDARD SEPARATION WHEN ATX-LTT DESCENDED ON VISUAL APCH CLRNC FROM MMNL AND CONFLICTED WITH AN ACFT IN ZHU AIRSPACE ENROUTE OVER LRD.

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ON 11/WED/88 LTT X; WHICH I WAS COPLT; WAS RETURNING FROM MEXICO CITY; MEXICO; TO LAREDO; TX. WE WERE AT FL310; AND REQUESTED BY MONTEREY CENTER TO DSND TO FL240. MONTEREY CENTER THEN ASKED US TO STOP OUR DSCNT TO FL260 FOR A SBND LTT Y. AFTER CLRING THE LTT Y WE WERE THEN CLRED TO FL240; THEN ON DOWN TO 7000'. AT AROUND 11000' MONTEREY CENTER HANDED US OFF TO NUEVO LAREDO APCH WHICH CLRED US TO 5000' AND TOLD US TO RPT THE MEXICO/U.S. BORDER OR CALL LEVEL AT 5000'. WE RPTED THE MEXICO/U.S. BORDER AT ABOUT 7000' AND ABOUT 7 NM FROM LRD AND SAID WE HAD THE ARPT IN SIGHT. NUEVO LAREDO APCH THEN CLRED US FOR THE VISUAL APCH AND TO CONTACT LRD TWR. WE CONTACTED LRD TWR AND RPTED THE ARPT IN SIGHT; AND THEY CLRED US FOR A STRAIGHT IN LNDG TO RWY 35R. THE NEXT THING THAT HAPPENED WAS LRD TWR ASKING US WHETHER WE WERE VFR WHICH WE REPLIED 'YES.' THEN LRD TWR ASKED IF WE HAD CANCELLED OUR IFR; WHICH WE REPLIED; 'NO;' BECAUSE WE WERE CLRED FOR A VISUAL APCH. AFTER LNDG AND SECURING THE PLANE AT THE CUSTOMS RAMP; WE WERE REQUIRED TO CALL THE TWR. LRD TWR SAID THAT ZHU RPTED THAT WE HAD BROKEN OUR LAST ASSIGNED ALT. WE BELIEVE THAT NUEVO LAREDO APCH CLRED US FOR A VISUAL APCH AND THAT LRD TWR CLRED US FOR LNDG. I BELIEVE THAT NO ALT WAS BROKEN AND THAT BETTER COM IS NEEDED BTWN THE MEXICO/U.S. CTLRS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: WHEN THIS FLT CREW MADE TELEPHONE CONTACT WITH ZHU; THEY WERE TOLD THAT WHEN THEY CROSSED THE U.S./MEXICO BORDER THEY CONFLICTED WITH AN ACFT BEING CTLED BY THEM. SINCE STANDARD SEP WAS LOST; ZHU WAS REQUIRED TO START ENFORCEMENT ACTION AGAINST THEM BECAUSE THEY HAD DSNDED W/O CLRNC. THE RPTR EXPLAINED TO THE ZHU SUPVR THAT NUEVO LAREDO HAD CLRED THEM FOR A VISUAL APCH; BUT THE ZHU SUPVR SEEMED NOT TO BELIEVE THIS. SINCE THIS INCIDENT; THE FLT CREW HAS HEARD NOTHING FURTHER FROM THE FAA. RPTR HAS CONCLUDED THAT THE ZHU SUPVR LATER CONTACTED NUEVO LAREDO APCH CTL AND FOUND THAT THE PROB WAS NOT CAUSED BY THE FLT CREW BUT RATHER BY A LACK OF COORD FROM NUEVO LAREDO.