Well, it fits an SMLE, it was tested and approved for service, inspected a second time in 1918 or 1919, then given away to someone who wrote Arabic and had a bunch of them: this one is Number 938.
Being that Turkey lost the war, I would be looking toward one of the new Armies being set up under British occupation: Hejaz, Mespot, Transjordan.
That said, I take the Fifth.