Thanks for translating for us.
As for the Geco barrel, no it would be a replacement barrel. For two reasons, Geco only is known to have supplied one firm directly, Gustloff Werke Weimar in 1944, all others are depot barrels.
Secondly, and most importantly, is that Geco is not known to have made barrels before 1938, and when they were using the "cxm" code, these start in 1940, dropping their logo. Your barrel is probably 1940 or later, you would have to show the barrel code to know when it was made, the "40" in the code you typed might be the date the barrel was made or there might be more to the barrel code under the wood. I suspect the lot is "35" and the "40" is the date, primarily because I have never seen a 4 digit lot number from them (3540 would be an enormous lot number)
Image or type out the exact barrel code, cxm 3540 (what is after this? Should be a waffenamt e/26 and possibly a date), or is it cxm 35 40 (the 40 being separate from the "35"? If this is the case that is the barrel lot date)
Geco in 1940-1941 used "cxm" followed by a "lot number" then a date, then the waffenamt. You might look for an "0,2" on the barrel shoulder, as this is typical of depot re-barrels.