Hello Lowlander !
Thank you for your advice !
I tried this, by converting the WMA to an MP§ and adding it to the library, and by replacing the WMA with an also converted WMA (newer format) with exactly the same name. But none of them was listed in the list of files with "Unsynchronized Tags" from where I could select them and use the function you described.
Also just selecting the new file and using the function didn't change the content of the tags.
And I should mention that the converted files included most of the tags from the old file, just Date, BPM, Songtext, and other composers or artists where missing if more then one (sepereated with semicolon) was entered in the tag before, obviously a missing feature of the converter I used, which can not copy every tag.
Thats probably the reason why MediaMonkey didn't take information from the library but updated it with the content of the tag in the new file.
If you have any more suggestions the are very welcome