What was found
ON RAMP, FUEL 300LBS, LT TANK HEAVY. CROSSFEED TO LT TANK UTILIZED ON TAXI OUT. FUEL IN NORMAL POSITION ON TAKEOFF. 220 LBS HEAVY ON THE LT TANK. CLIMBING OUT, LT CROSSFEED SELECTED & FUEL USED DOWN TO BALANCED. CROSSFEED SELECTED OFF. CLIMBING UP TO FL340. LEVEL AT FL340 NOTICED FUEL BECAME INBALANCED IN OPPOSITE DIRECTION OF 120 LBS HEAVIER ON RT SIDE. CROSSFEED TO RT SELECTED. INBALANCE INCREASED TO 160, THEN 200 LBS. & LT TANK BEGAN TO DECREASE 20LBS EVERY FEW MINUTES. ATC ADVISED OF ISSUE. DIVERTED TO PBI (DJT) & BEGAN A DESCENT DOWN TO FL200. AFTER A WHILE, FUEL BECAME BALANCED AGAIN, CROSSFEED TURNED OFF & CONTINUED TO PBI. SINCE FUEL SYS NOW OPS NORMAL, ADVISED ATC, WOULD NEED TO BURN 700 LBS TO GET BELOW LANDING WEIGHT. HELD FOR 3 TURNS WITH FLAPS 1 & GEAR DOWN. ONCE UNDER LANDING WEIGHT, LANDED AT PBI (DJT) UNEVENTFULLY. REMOVED, CLEAN & RE-RACK BOTH FUEL CONTROL PCBS NZ107 AND NZ207. FOLLOWED UP WITH ENG RUNS & ATTEMPTED TO SIMULATE CREW'S WRITE UP. PERFORMED FUEL CROSS FEED VALVE OPS CHK, CHKD SUCCESSFULLY, NO ISSUES ENCOUNTERED, KEPT ENGS RUNNING & WAITED 10 MINS WITH CROSSFEED OFF & WAS NOT ABLE TO ENCOUNTER ANY ISSUES OR DEFECTS WITH THE FUEL SYS (LT 3580 & RT 3580). POWERED DOWN & LET ACFT TO SIT FOR 4 HRS, CHKD TO SEE IF FUEL MIGRATED TO EITHER TANK. RAN ENGS & PERFORMED ANOTHER SUCCESSFUL FUEL CROSSFEED VALVE OPS CHK, POWERED DOWN & LET SIT FOR ANOTHER 4 HRS & POWERED UP TO FIND FUEL STILL DID NOT MIGRATE. FUEL SYS NOW CONSIDERED FULLY FUNCTIONAL & OPS. WORKED IAW AMM 28-20-00.