Cody,
There are at least two instances that prove the use of the MP43/44 in Normandy. One that can't be refuted is a photo of a grenadier of the 2nd Panzer Division marching with one slung around his neck.
The other is anecdotal, of a GI unit finding one during Operation Cobra.
Certainly, these weapons weren't thick on the ground in June 1944, but it would seem that some German units that joined the Normandy fighting a bit later certainly did bring a few with them. I suspect that one wouldn't see a whole section equipped with them though.
HTH,
Ron V
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