As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
WHILE JUST BEGINNING A DECENT FROM FL450 THE THROTTLE WAS REDUCED SLOWLY AND TOGETHER ON BOTH ENGINES, THE RIGHT ENGINE ROLLED BACK TO FLAME-OUT. ENGINE WAS RE-STARTED SUCCESSFULLY AT FL220 AND REMAINED RUNNING AND OPERATING NORMALLY THE REST OF THE FLIGHT TO LANDING AT KHPN WHITE PLAINS, NY. FADEC DATA WAS DOWNLOADED AND SENT TO WILLIAMS BY WAYNE TOHER OF RELIANT AIR. WILLIAMS CONCLUDED THE FUEL DELIVERY UNIT FAILED. FDU WAS REPLACED BY TEXTRON/CESSNA IN WHITE PLAINS AND WELL AS THE OTHER ENGINE (LH) FDU BY DEMAND FROM RELIANT.