FXE CTLR EXPRESSED CONCERN REGARDING MIA TRACON'S NON COMPLIANCE WITH LOA.

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I WAS WORKING CLRNC DELIVERY AT FXE AND MONITORING LCL CTL. LCL CTL WAS BUSY AND THERE WAS TRAINING BEING CONDUCTED ON THAT POS. CLRNC DELIVERY HANDLES COORD BTWN MIA; THE OVERLYING APCH CTL FACILITY; AND FXE. I SAW AN LJ55 THAT WAS N OF THE FIELD ON THE DOWNWIND AT 3000 FT. THE LJ55 WAS BEING VECTORED FOR A VISUAL APCH TO RWY 8 BY MIA. THE LOA BTWN MIA AND FXE STATES THAT A VISUAL APCH DOES NOT NEED TO BE COORDINATED AS LONG AS THE ACFT IS ESTABLISHED ON A 7 MI FINAL. MIA DISREGARDED THE LOA AND TURNED THE LJ55 ON A 4 MI BASE WITHOUT COORD. LCL CTL HAD NUMEROUS ACFT IN THE PATTERN; AND TO AVOID CONFLICT WITH THE LJ55; TURNED A C172 ON THE BASE BACK TO THE DOWNWIND; CAUSING THE C172 TO MAKE A SHARP TURN TO AVOID THE LJ55 THAT WAS DSNDING AND AT A SPD OF ABOUT 200 KTS ON THE BASE. THE LCL CTLR ALSO NEEDS TO TURN ANOTHER C172; THAT WAS CLRED TO LAND AND ON A 2 MI FINAL; BACK TO THE DOWNWIND SINCE THE LJ55 GAINING ON THAT C172 AT A HIGH RATE. THE ACTIONS OF THE CTLR AT MIA RESULTED IN A DANGEROUS SIT. DUE TO THE QUICK ACTION OF THE LCL CTLR AT FXE; THE SIT DID NOT CAUSE LOSS OF SEPARATION. I THEN CALLED MIA TO ADVISE THE CTLR THAT COORD WAS NEEDED FOR A VISUAL APCH OF THAT TYPE. THE MIA CTLR RESPONDED BY SAYING 'OH.' I THEN NOTIFIED MY SUPVR OF THE INCIDENT.