What was found
WHILE CRUISING AT FL400 THE LEFT ENGINE ROLLED BACK. IMMEDIATELY, I TRIED TO MOVE THE THROTTLE TO A DIFFERENT POSITION TO SEE IF I HAD ANY AUTHORITY. I DID NOT. I DECLARED AN EMERGENCY WITH ATC AND STARTED A DESCENT TO KEEP THE SPEED UP. I DECIDED TO DIVERT TO KLNK BECAUSE WE HAD JUST RECENTLY PASSED OVER IT, THE WEATHER WAS IFR, AND THEY HAVE A LONG RUNWAY. THE CHECKLIST WAS RAN TO COMPLETION. WE DID NOT ATTEMPT A RESTART BECAUSE THE RIGHT ENGINE WAS RUNNING SMOOTH AND SARA HAD NOTICED SOME VIBRATIONS EARLIER IN THE FLIGHT. WE LANDED 18 AT KLNK AND TAXIED INTO ATLANTIC. THE FIRE TRUCKS ESCORTED US AT 50%. TO GET THE LEFT ENGINE TO SHUT DOWN I HAD TO MOVE IT OUT OF CUTOFF AND THEN BACK TO CUTOFF. NO FURTHER COMMENTS. WE HAVE TO PARTS THAT CAUSED DIFFICULTY LET, DUNCAN AVIATION IN LINCOLN, NE IS CURRENTLY T/S THIS EVENT.