A C560XL CREW; ON FINAL TO FFZ; HAD AN NMAC WITH TFC THAT WAS SUPPOSEDLY PRECEDING THEM ON FINAL.

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PHX APCH CTL CLRED US FOR A VISUAL APCH TO RWY 4L AT FALCON. WHEN WE CONTACTED FALCON TWR; WE WERE TOLD TO ENTER A 3 MI FINAL FROM A R BASE TO RWY 4L TO FOLLOW A NAVAJO ON A L BASE TO RWY 4L. WE THEN ADVISED FALCON TWR THAT WE WOULD WIDEN OUT THE FINAL EVEN FURTHER THAN 3 MI TO LOSE ALT FROM A LATE CLRNC FOR THE VISUAL APCH. WE DID NOT SEE THE TFC AT THIS TIME. FALCON TWR ADVISED US TO DEVIATE L AS FAR AS NEEDED; BUT TO MAINTAIN CLRNC FROM THE MOUNTAINS. WE THEN TURNED A 5 MI FINAL TO RWY 4L AND CONTINUED INBOUND. FALCON TWR POINTED US OUT AS TFC ON A 3.5 MI FINAL TO ANOTHER ACFT. SHORTLY AFTER THIS CALL; WE GOT A TA ON OUR TCASI. WE; THEREFORE; SHALLOWED THE DSCNT AS AN EVASIVE MANEUVER AND CONTINUED TO LOOK FOR THE TFC. WE THEN SAW THE NAVAJO BREAK OFF FROM UNDERNEATH US IN A CLBING L TURN. WE WERE CLRED TO LAND #1. AFTER LNDG; MY CAPT CONTACTED FALCON TWR BY PHONE TO DISCUSS THE SIT. THE TWR ADVISED HIM THAT THE NAVAJO WAS FLYING A MUCH LARGER PATTERN THAN THEY EXPECTED AND THAT THEY HAD LOST SIGHT OF THE NAVAJO. THEY ALSO STATED THAT THERE WAS A COM BARRIER DUE TO THE NAVAJO PLT'S ENGLISH NOT BEING SO GOOD. SUPPLEMENTAL INFO FROM ACN 562358: I SPOKE TO THE TWR ON THE PHONE AFTER LNDG AND WAS TOLD THE NAVAJO MADE A BIGGER PATTERN THAN THEY EXPECTED AND THEN THEY LOST SIGHT OF HIM AND TOLD HIM TO BREAK OFF THE APCH.