What was found
AIRCRAFT WAS GROUNDED: PILOT REPORTS WHILE ENROUTE IN ANU WHILE BURNING FUEL FROM CENTER TANK, RIGHT MAIN TANK QUANTITY DECREASED VERY SLOWLY TO ABOUT 500 LBS IMBALANCE BALANCE TANK STABILIZED. NO NOTICEABLE ROLL IN AIRCRAFT UPON GATE ARRIVAL. IMBALANCE DECREASED TO WITHIN 300 LBS BETWEEN TANKS 1 AND 2 UPON ENGINE 2 SHUT DOWN ENGINE FAIL ANNUNCIATED ON NO.2 EGT. MAINTENANCE REMOVED AND REPLACED FUEL QTY PROCESSOR IAW AMM 24-41-81. ACCOMPLISHED INSTALLATION TEST AND BITE IAW AMM 24-41-00. NO FAULTS NOTED . OPS CHECKED GOOD.