The Germans did that primarily with the weapons of Nations they had conquored (many of the German troops on the Atlantic wall were armed with French Betherier rifles and Lebel revolvers, for example) or in the case of Russia, where they had captured enormous amounts of equipment.
As I said, it's a long shot. I have heard of 1911's that were captured and re-issued in very small numbers, but they were not preferred primarily because they were difficult to obtain ammunition, magazines, and other such accoutrements for. You are correct that guns and ammo from either conquered enemies or the eastern front were issued more liberally and I would venture to guess that's because ammunition and accessores were much more avialable than they were for captured U.S. and British weapons.
Smith, and Wesson, and Me. -H. Callahan
Well waddaya know, one buwwet weft! -E. Fudd
All bad precedents begin as justifiable measures. -J. Caesar