While all the expressed opinions contain information that has some merit ...I absolutely must concur with Dwight. Attaching a stock to this gun would NOT be legal under any circumstances.
The "basis" for the gun is the serial numbered and controlled Frame. It was NOT manufactured by either of the Luger producers of the Artillery Model. I wouldn't want to have to defend this situation in court...
The gun is NOT an artillery model... just a reproduction of an artillery model. This gun could not appear to fall in a category as listed in the C&R list that is exempted from the NFA.
In order for the gun to be technically legal with a shoulder stock, it would have to be made with both a frame and an upper receiver (barrel extension to some) that falls in the correct serial number sequence to have been an artillery, and that was produced by either DWM or Erfurt. It would then be considered a "rebuilt" or "restored" or "repaired" artillery model that no one could question it's origins.
IMHO, to recommend any other course of action might be reckless... and I would not want to be responsible for someone wearing handcuffs for following my advice. I have to err on the side of safety in these circumstances...
That's my story and I'm sticking to it.