George was a Corporal in the 14th Batallion of Highland Light Infantry. Occupation listed as a musician.
I can only imagine he was stationed in Scotland after the war. His usual residence is listed as a farm in Portsmouth (possibly a workhouse farm).
His parents, as you rightly pointed out, were both deceased. They obviously died late enough into his childhod for him to remember them as they are both named on his marriage certificate (I can email this to you). His father, James Cooper, was a bricklayer and journeyman. Your great-grandmother's name, I cannot make out. You may have some luck with this on ancestry.com.
Your grandparents were married at The Manse in Galston, Ayrshire, on March 4, 1919.