Narrative:

Preflight; takeoff and initial phases of flight were normal and uneventful. While at FL380 and approximately 150 miles west of ZZZ; I decided to empty the center tank of 800 pds that had migrated during the flight. Also we had a 900 pd imbalance between the left and right wing tanks that I wanted to equalize. Just seconds into the cross feed we got a 'left fuel system lo press' EICAS immediately followed by the left engine rolling back and flaming out. I took control of the aircraft and first officer retrieved and ran the in-flight engine restart checklist. Simultaneously; I coordinated with ATC a decent to FL340. By the time we reached [flight level] 340 the engine was restarted and at idle with all indications being normal we slowly brought the power to a cruise setting. All indications remained normal and within parameters. Aircraft control was transferred back to first officer and I contacted [operations control]; [maintenance control] and captain (on duty) via airinc. After conferencing with all; we agreed the best and safe course was to continue to ZZZ1. The flight continued and terminated in ZZZ1 without further incident.

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Original NASA ASRS Text

Title: B-767-300 pilot reported inflight engine shutdown during cruise.

Narrative: Preflight; takeoff and initial phases of flight were normal and uneventful. While at FL380 and approximately 150 miles west of ZZZ; I decided to empty the center tank of 800 PDS that had migrated during the flight. Also we had a 900 PD imbalance between the left and right wing tanks that I wanted to equalize. Just seconds into the cross feed we got a 'Left fuel system Lo Press' EICAS immediately followed by the left engine rolling back and flaming out. I took control of the aircraft and First Officer retrieved and ran the In-flight Engine Restart Checklist. Simultaneously; I coordinated with ATC a decent to FL340. By the time we reached [flight level] 340 the engine was restarted and at idle with all indications being normal we slowly brought the power to a cruise setting. All indications remained normal and within parameters. Aircraft control was transferred back to First Officer and I contacted [Operations Control]; [Maintenance Control] and Captain (On Duty) via Airinc. After conferencing with all; we agreed the best and safe course was to continue to ZZZ1. The flight continued and terminated in ZZZ1 without further incident.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.