Mystery Carcano w/ Luftwaffe Markings

I everyone, I'm brand new to the forum but decided to create an account specifically for this question.

I used to work at a gun store and when I was there, a woman came in with an old Italian Carcano Model 1938. She was looking to see how much it would be worth. However, as you'll read and see, I couldn't tell her. She told me her grandfather brought it back from Europe during the war. She told me he picked up this rifle in Germany. I know the Volkssturm used a ton of Carcanos, but the markings on the buttplate are what threw me off.

On the buttplate is the German abbreviation for Aufklärungsgruppe 122, which was an aerial recon squadron stationed in Italy during 1944.This is the first time I've ever seen something like this. Was it common for Luftwaffe units to inscribe their unit designation and tour of duty on rifles? Why a Carcano? How did it make it back to Germany?

Any info you guys could give me would be greatly appreciated.

Looks like it was done as a memento or presentation, not as a property mark. Lots of these were available, auxiliary guards at LW sites (guarding airfield infrastructure, or airfield repair units for example) often had second- or third-line weapons issued long before it got so bad that Volksturm were formed, so these would not be hard to find.

Thanks for the reply. That's what I was thinking happened as well. But I was just interested to see if there was anything else.