thank you very much! The Problem is already solved, here a sort overview about the solution:
I don't use the traditional (dowload from your website), i just use the store (bridged) version.
Other browser extensions working very well (for example Edge and Chrome).
With your suggestions for troubleshooting i could analyse that on a working machine there was a open Socket for the NMHost.exe but on the problematic machine not.
The Problem was that on the working machine the user which installed the NMHost.exe is the same user which use enpass. The user has administrativ privileges.
On the problematic machine the user which use enpass doesn't have administrativ priveleges.
Installing NMHost with a different user as the one which uses enpass seems to cause this problem.
So i just gave the user which uses enpass administrative privileges on the problematic machine for installing NMHost and removed them afterwards.
Now the connection to Firefox works fine (even without administrative privileges on the machine)!