Oh that's a TAPER - OK. I'm with you now. If it were me, I'd consider turning off the tapered part of the barrel on a lathe or in the vise, otherwise you will have a pretty long threaded part, making your muzzle device need a longer threaded section. May or may not be a problem for you.
What you need to do is measure the OD of the barrel. That will give you the max size you can thread. If it is 15mm then you could thread it with the 15x1 RH threads that HK uses and any HK muzzle device. My G3 has a typical M16 style birdcage flash hider. Not sure what the FAL is but I think it is 9/16 something... that would give you many choices, along with the potential of "converting" it to something you'd prefer...