I don't know of any barrel drawings that are public. Depending on the barrel profile your friend has, it might not be worth it to try to make it look original. A lot of work would be needed. A problem you might encounter is that some european AUG barrels are a different length than the typical US barrels (16.5", 18", 20", and 24"). I guess if you had a 22" barrel or whatever the mm equivalent is, then you could chop it down. To make it as close to a military barrel as possible you would also want to thread the exterior of the barrel. Fortunately I do know the exterior thread pitch - M18x1.5mm RH. With the US barrels, there is a slight difference in the length of muzzle threading area and the non-threaded step down between the shoulder and the threads. Whether it varies due "Friday at 5pm" made barrel or what, I don't know, but they are different.
I'm not a machinist and I wouldn't be a good source to get precise measurements from, perhaps someone skilled in the use of a dial caliper can step in with exact dimensions? Or you could just thread it for one of many AR type muzzle devices...
Best of luck.