Very strange your Beretta '34: look like a gun produced on 1940/41 (RE and IVU) that was completed and serialized on July or August 1943. And also the slide look like the writing was erased (there are some shadows and we can read Beretta ...) and then refinished.
The holster is one of these produced "German style" with the Italian leather after the September 1943 but this don't say who used it.

 

Thanks for the info on the holster.

Here's another shot of the blank side. There are two small nicks. I don't see the Beretta logo you mentioned but I do see two men walking through the Gobi desert at sunset looking for a bar

 

Holster's legit WWII Italian. Package value? $800–$1,200 easy for a rig this mint.

 

Thank you. Is it common for the magazine release spring to be so firm? I'm pretty strong and I have to give it a good thumb shove to get it back.

 

I might question if this pistol has the original finish. A few clues: The red dot under the safety is missing. And the Crown/RE on left tang looks to have also rust damages under this layer of blue. Or is that grease-oil smears? There are other areas of concern as well. Just enough that I would request more images if I were bidding. As to the value ?? Perhaps $600-$800 today would not surprise me, and more if a closer look was allowed. There are many offered in this serial range with minimal wear making the competition pretty stiff in the $1000 range.

I apologize if I over stepped your RFI.

The magazine release can be a struggle. I'd place this as a 1943 production based on serial nr. and other features.

 

When a really nice speciment of an old gun comes in, it's always a suspicion that it's been refinished.

I own a lot of guns and I have refinished and restored a number of guns. If this is a refinish, it's the best one I've ever seen. You can actually see the edges lifted on some of these stamps. I don't see rust anywhere on or below the surface of this finish. Also, the polishing/machine marks of the original finish are consistent throughout, with no cross polishing marks or attempts to remove them.

There is some wear to the edges, but it's no a refinish.

 

Check out the consistency of the machine marks on the backstrap. Hope you can see the tiny horizontal lines on it and the vertical lines on the frame.

 

The holster is 100% legit, I've had more than a few. Never really liked these "one size fits all" things, they are always too long in the nose. The pistol is a tough call. From where I sit, I'd give it 50/50 chance on the slide being buffed and refinished and the frame just refinished without buffing. If it's the case, it was done long ago. As far as value goes, I've sold these holsters for around $100 give or take a few $$, the pistol I would pass on, unless sold at a shooter-grade price.