Saab Captain reported the number 1 engine shut down in flight and could not be restarted. The flight crew performed a successful diversion to a landing.

Narrative

Myself and my Copilot were operating a flight departing from ZZZ1 enroute to ZZZ2. Approximately 40 minutes after takeoff; while at a cruise altitude of FL310 we felt the airplane begin to mildly shake as though we were encountering light turbulence. We began to scan the gauges and performance pages to see what was happening. After 4-5 seconds of shaking; we heard the engine start shutting down. As we were pulling up our engines data page; we began to receive multiple EICAS messages informing us that our left engine had failed. We performed our memory items to secure the motor then performed the appropriate checklists for the remaining warnings/cautions. At this point the only thing we have noticed wrong with the motor is that the oil quantity on the #1 engine (left) is reading yellow. All other temps; fluids; and pressures where still within normal operating ranges. Copilot and I then discussed the next course of action. We began a slow descent to keep a safe airspeed and prepare for a possible emergency landing. After a few seconds of the engine being completely shut down the oil quantity quickly climbed back up to a normal operating range. We decided after considering all factors to attempt an engine restart in flight. We performed the appropriate checklist and started the engine back up. The engine started successfully but when we attempted to take the prop out of feather and into normal RPM; it would not come out of feather. At this point we decided to land and have the engine looked at by Maintenance. We [advised ATC] and began a descent into ZZZ. I made an announcement to the passengers and flight attendant informing them of our situation and change of destination then coordinated with ATC. We descended and made a visual approach to Runway XXC at ZZZ where fire trucks and other emergency personnel were waiting for us. After a successful landing we exited the runway and came to a stop. Tower asked us of our intentions; and we said that we would like to secure the emergency and taxi into the FBO. We were escorted into the FBO by fire trucks. After shutting down the engines I called my company and began informing the appropriate employees/managers of the current situation.