As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
ENGINE FLAMED OUT ON SLOW DESCENT BELOW 37,000 FT. LOW PRESSURE FUEL LIGHT FLASHED THEN BOOST PUMP AS ENGINE FLAMED OUT. ENGINE WAS RESTARTED ON FIRST TRY IAW PROCEDURES AT 10,000 FT. NO EMERGENCY WAS DECLARED. ACFT LANDED SAFELY. ENGINE WAS INSPECTED AND FUEL DELIVERY UNIT WAS REPLACED IAW SB FJ44-73-044R3. GROUND RUNS PERFORMED SATISFACTORILY AND CREW FLEW ACFT ON OPS CHECK FLIGHT WITH NO DEFECTS. ACFT RETURNED TO SERVICE.