What happened
The FAA’s narrative, in sentence case. The FAA writes it in capitals and removes private details.
(-5)During climb out of FL390, 100 miles east of anchorage, AK, the right eingine on N430JW compressor stalled and failed. Unable to maintain altitude the aircraft was forced to descend. The pilot initially requested lower and was assigned FL350. The pilot did not declare an emergency, but notified the controller that he had lost an engine and was going down. The controller declared an emergency for N430JW. During descent IFR separation was lost between N430JW and an Alaska airlines flight. At the time of the incident separation was estimated to be 4 miles horizontal and 1500 feet vertical.
As the FAA filed it
(-5)DURING CLIMB OUT OF FL390, 100 MILES EAST OF ANCHORAGE, AK, THE RIGHT EINGINE ON N430JW COMPRESSOR STALLED AND FAILED. UNABLE TO MAINTAIN ALTITUDE THE AIRCRAFT WAS FORCED TO DESCEND. THE PILOT INITIALLY REQUESTED LOWER AND WAS ASSIGNED FL350. THE PILOT DID NOT DECLARE AN EMERGENCY, BUT NOTIFIED THE CONTROLLER THAT HE HAD LOST AN ENGINE AND WAS GOING DOWN. THE CONTROLLER DECLARED AN EMERGENCY FOR N430JW. DURING DESCENT IFR SEPARATION WAS LOST BETWEEN N430JW AND AN ALASKA AIRLINES FLIGHT. AT THE TIME OF THE INCIDENT SEPARATION WAS ESTIMATED TO BE 4 MILES HORIZONTAL AND 1500 FEET VERTICAL.