When I dug out my sales receipt from 1992, it was for a 1917 Luger. So, it could have been for a Luger carbine. I have both a 13" and a 16" barreled receiver for this Luger, so here's the period buttstock for it.
Finding a buttstock was very frustrating. I wanted a '1902 style' profile but all I could find were '1920 style' repros or duplicates. So, I ended up getting a used semi-finished 1920 style and sectioning & gluing it to look like a 1902 style.
(1) Buttstock as received from eBay seller.
(2) Milling a .060" thick x 10mm Walnut 'popsicle stick' for stock iron groove, both top & bottom.
(3) Popsicle sticks glued in & being milled to fit iron.
(4) Milling butt flat, and at an angle like 1902.
(5), (6), and (7) Milling lever reliefs in gooseneck with ball end mill.
(8) Stock iron fitted.
(9) Sawing eBay buttstock in half. EEK!!! What is this madman doing???

(10) Sawed pieces. Actually, two saw cuts, to create a ~5/16" taper/drop to the stock

(11) Milling sawn end of stock flat.
(12) Milling 3/8" slot for reinforcing wedge.
(13) Milling sawn end of gooseneck flat.
(14) Clamping stock pieces together to mark gooseneck for slot.
(15) Milling 3/8" slot in gooseneck.
(16) Pieces slotted and stacked to admire.
The slots have been milled at different angles, so the filler piece cab be wedge-shaped. Maked fitting easier.
(17) Milling a piece of Walnut down to .375".
(18) Clockwise - Spare piece of 3/8" Walnut; cardboard form; 3/8" wedge inserted between two sawn pieces.
(19) Wedge & two pieces glued together with Resorcinol glue and left clamped under mill quill.
(20) Glued buttstock 24 hours later, ready for shaping.