Your pictures are less than ideal, but with your description it is clear this is an ordnance rework, an extensive one by the looks of it... the barrel and stock are ordnance spares, the barrel made by Fritz Werner, a very important machinery maker (which probably made some of the machines that made the rifle parts... most metal working firms had some of their machines on hand, at least ones big enough to afford them. They had two facilities, one of which made rifle barrels during the war.). While Fritz Werner barrels usually have lots or dates, or both, there are two others that are just like yours, with neither. Too few are known to determine where these fall in time wise, but I suspect early, - most are dated 1943 or have late style lots. That these have neither suggest these are the first they made, but that is speculation based upon a limited number of observations and the trends of how the others operated.
The markings on this last post show the byf and acceptance for the ordnance status of the stock, the small indecipherable stamp is of the depot that did the work. The manner of the x'ing out of the buttplate is distinctive of at least one firm, think it was Posen, also the small nature of the depot acceptance is similar to their stamp. You really should take a close look at the stamp, see if you can make out any characters under the eagle (it is a small eagle over letters and numbers, Posen is often Psn); they were a prolific reworker in the mid-war period, if I had to guess on the depot, it would be Posen, but others are possible.