Gta Vice City Files Backup

I found my save games from a long time ago on a windows machine and I'd like to play them on Ubuntu.
I've got GTA Vice City running just fine with wine, but GTA never finds my save games and I cannot save new games either because the games are gone when I want to load. That's probably a permission issue or a non-existing folder issue.
Where am I supposed to copy my saves, or where are saves stored with wine?
In Windows it was My DocumentsGTA Vice City User Files. Wine has My Documents configured as ~/. But ~/GTA Vice City User Files does not work for GTA.
I own all files and folders and have write permissions. I am missing something.