Air carrier Dispatcher reported the flight crew reported a left engine fire during climb. After dumping fuel; flight returned to departure airport and performed an overweight landing.

Narrative

Crew called via satellite phone reported. They were given a climbed to FL310. When the started the climb they heard a loud pop then got a left engine fire EICAS message. Followed checklist. Pulled the fire extinguisher bottle message went away. Reported they had shut the engine down. Wanted patch with Maintenance Control. And plan return to ZZZ. Flt had been airborne approx 30-40 mins. I gave the crew landing runway limit weight along with performance limits weight. We discussed dumping fuel vs landing overweight. Everyone agreed to dump fuel to be lighter for landing. Flight landed safely back in ZZZ. Did land approximately 10.0 overweight. Flight did not delay arrival to dump more fuel since we were under runway and performance limit. Since not 100 percent sure what happened to engine.[Requested priority]. Equipment rolled in ZZZ. My only concern here is crew called into Chief Pilot. I had asked to speak with crew if they called them 1st. Was not patched into crew or crew was not transferred to me. I ended up having the Chief Pilot call the Captain back and request he call me for fuel dump info. And for brief of event. Captain did call and irregular message completed.