I could successfully install drivers for this module thanks to this answer, but there are some issues.

I need bluetooth for my keyboard, which works just fine under Windows. But with linux connection can often drop, and also very often some letters are typed much more then they needed.

Example:

Likkkkkkkkkke tttttttttttthhhhhhhhhhhhhhhhhatt!!!!!!!!!

Often after that loops it disconnects. If i am turning off the keyboard during that loop, it will still continue to type for a long time, that is why I am sure, that it is a linux drivers issue.

Any ideas please how to make work more stable?