Can I ask a favor of you???? You have a fsu marked rear cover. I hope that yours is original as you are stating and I'm hoping.. Could you Please review your Lafettes front leg looking for the fsu mark or the triangle with S323 in it. As I'm not sure if fsu marked the front leg or not or where you may or may not find a marking, but please look for it.
Here is a link to pics of where ecy marked theirs.viewtopic.php?f=25&t=13798
Also when I looked at your well marked fsu rear cover I noticed what I think is a fsu mark on the (looking forward) front right side rear weapon mount hook.
Here is how mine looks.
Should also note yours looks like one of the early Lafettes that was made for the MG42 only. Note the lack of an additional cut so it could have fit the MG34 Grip. Mine is a converted MG34 to MG42 Lafette, that is why you see the additional cut on the front.