Hello Mikkel, Welcome to the Luger Forum!!
The byf 42, S/N 3581b was completed about February of 1942, within a month. Your guess of March was a good one!
All military Mauser Lugers were shipped with two magazines that matched the serial number of the pistol until about July of 1941. After that, which coinsides with the Lugers containing a "U" Suffix, the magazines were either blank aluminum bottom fxo or black plastic bottom fxo types.
The black plastic bottom fxo magazine is correct for your byf 42.
Disassembly of this magazine is difficult, without damaging the plastic material. I would recommend you immerse the metal parts in a good gun solvent, like Hoppe's No. 9 if you can get it, then either air blow or air dry it. This should get much of the grease and grime from the inside surfaces. You may have to repeat this process several times to complete the cleaning.
Good Luck!