This should work with one caveat: `*.fastresume` files specify the absolute path for torrents and they are naturally incompatible with Linux.
How I'd approach that:
* Do not use or copy this directory
* Download and open the appropriate torrent files again
* Specify the save path where they are already downloaded to, **uncheck** "Start now" (it should be unchecked by default)
* Right click the torrent and choose "Force recheck"
Now you can start seeding or continue downloading it.