Purple, please don't take this the wrong way.
An uncle of mine, that was killed in a tractor accident in Saskatchewan 35 years ago, fought in North Africa, Italy etc.
The unit he was in highly frowned upon using or carrying battlefield pick up firearms. Things happen and firearms get broken, lost or quit working. The troopie, did what he had to do and made do with what came to hand.
If they wanted a souvenir, they had to turn it in to someone to be recorded and if accepted, sent back home. He sent two pistols home as well as some other stuff. Some of the things he turned in, were either high graded or refused. Mostly, they were personal items from a fallen foe. Rings, watches, paybooks, personal photos, that sort of thing.
Wearing enemy clothing was strictly forbidden. The only thing they made the exception for was the White winter camo smock that were quite prized. The Canadian wool uniforms tended to soak up water and gather frozen snow very well. Not only that, the smocks were quite similar to their own.
They were encouraged to familiarize themselves with axis weapons, during lulls or after being pulled back.
When it came time to be shipped home, if you had an unauthorized weapon in your kit and managed to get caught with it, you got to spend another six months in Europe on occupation duty.
I wish I had access to some of the pics in his scrap book. He managed to be unlucky enough to be the one in five selected to have his bag inspected and was caught with a pistol. In the six months of occupation duty, he took many pics. He had a rescued German camera and managed to get ahold of a lot of film.
He had dozens of pics of destroyed German, Italian and Austrian towns. Nothing from Africa at all. One thing that always amazed me, were the piles of small arms laying in the streets. There were also piles of ammunition of all sorts.
The piles of small arms, weren't just axis arms. There were Russian, Italian, British, Austrian, US, French etc. He didn't know if the Germans had used them or if they were from captured stores or from fallen allied troops. Just that there were thousands upon thousands of them. Everything from pistols on belts in holsters to smgs, rifles, hand grenades, panzerfausts etc. You name it, it was likely there.
The people in the area, couldn't care less about them and didn't bother with them, other than a few kids and thugs. There was also a strict prohibition against being in unauthorized possession of firearms while under Martial Law.
Anyway, he wasn't allowed to search through those piles. No souvenirs, after armistice was official. I'm sure a lot of stuff slipped through but one thing he did mention, was that entrepreneurs from all over Europe and the rest of the world, were checking this stuff out and either putting claims on it or bidding on it.
I suspect that most troopies using captured equipment were reequipped when moved back from the front for R&R or to be moved to another area.