What was found
DURING CRUISE AT FL430 WITH RAT OF -39 RECEIVED AN AMBER ENG CNTRL FAULT L CAS MESSAGE. ALONG WITH THIS CAS MESSAGE WE RECEIVED THE R ENG. THE ENG CNTRL FAULT QRH PROCEDURE (U1) COMPLETED. PROCEDURE INDICATED TO LAND AND CONTINUED TO DESTINATION. DURING DESCENT, EXPERIENCED AN ENG SURGE & VIBRATION. SHUTDOWN RT ENG USING THE INFLIGHT ENGINE SHUTDOWN QRC. CONFIRMED RT ENG SURGING. AFTER RT ENG SHUT DOWN, EXPERIENCED SAME SURGE & VIBRATION COMING FROM LT ENGINE & DID AN EMERGENCY LANDING. REMOVED LT ENG. COMPLETED MX STAND BUILD UP OF REPLACEMENT ENG & INSTALLED THE REPLACEMENT ENG IAW AMM 71-00-05 AND EMM 71-00-00. REMOVED RT ENG. ACCOMPLISHED INSTALLATION OF NEW ENG IAW AMM 71-00-05 & EMM 71-00-00.