I don't have an Id, but you should be able to restore a windows library backup on linux MC. I'll try tonight and confirm, but my recollection is that it works. Restoring a library will get you your settings and metadata, but because the filepaths are different, everything will be broken at first.
The way to fix it is to make sure that the file path is the same beyond a certain point, and then use the "rename, copy, move" library tool. You'll want to select "update library location" instead of move or copy, and you'll want to use the find and replace function. Then you just fix the front part of the filepath.
So for example, if your music library is now at "C:\Users\Fre\My Music\..." and you'll be placing it in a linux filesystem "/home/Fre/Music/...", you'll want to use find and replace to replace all instances of "C:\Users\Fre\My Music\..." with "/home/Fre/Music/..."
That should fix your library. Make backups of everything along the way, and don't delete anything until you've got it working the way you want.