Heinrich,
The United States has laws forbidding the ownership of "short-barrelled rifles", that is, rifles with barrels less than 16 inches in length. In general, putting a shoulder stock on a pistol "creates" a short-barrelled rifle, according to the BATF. It is possible for a law-abiding American citizen to pay a small fee and obtain a license to own a short-barrelled rifle, but the fee must be paid and paperwork completed -before- making the attachment.
There are also laws concerning "curio and relic" firearms, that is, guns manufactured more than 50 years ago. This category has been created specifically to assist collectors in the ownership of firearms of a type which are unlikely to be used in the commission of crime.
There are detailed lists of specific guns less than 50-years old which the BATF considers "curios and relics" (some, but not all, of the 1970s Mauser Interarms Lugers, for instance), and some specific acceptable combinations of accessories. It is legal to attach an original or reproduction Artillery stock to an authentic LP-08; it is permitted to attach an original or reproduction Navy stock to an authentic Navy Luger; it is permitted to attach an Ideal stock/holster to a 1900, 1902, or 1906 American Eagle Luger (but -not- to the corresponding years' Commercial models!); it is permitted to attach a Carbine stock to an original 1902 or 1920 Carbine. It is not permitted to intermix them, a Navy stock on an LP-08, for instance.
Putting a stock on any other Luger is considered to be "making" a short-barrelled rifle, and is forbidden.
--Dwight