Private Conway was a member of Company B, 1st Battalion, 5th Infantry Regimental Combat Team. He was Killed in Action while his company was assisting the 15th Infantry Regiment, 3rd Infantry Division near "Outpost Harry" in North Korea on 12 June 1953.

Conway was awarded the Purple Heart, the Combat Infantryman's Badge, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.