No disrespect or correction was meant, wjkuleck, but your first Carbine is a Mauser Carbine, not a Luger - which was the pistol inquired about in the OP and shown in your second pic.
[Bob:] - wjkuleck's stock, pictured second, above, appears to be correct in every respect, AFAIK. I would think if it's numbered to the gun, a serial number or a partial number would be under the buttplate and/or on the buttstock attachment iron.
The Luger (Parabellum) pistols came with a few options.
Lugers were available cut/machined at the lower rear of the gripframe for a shoulder stock - which could be had on either a short barreled (4"-6") pistol (no forend), or a long barreled Carbine.
AFAIK, the Mauser Carbine only came the way wjkuleck's is pictured - the Mauser short-barreled pistols had a different frame with a hollow, blocky-looking, wood stock that doubled as a holster.
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