No guarantee that this will work, but you can try the following:
- Copy the game's installation folder from the Windows Steam library to the Linux one (the folder usually ending in
- Restart Steam and let it synchronize.
The binary files used by Proton are the same as on Windows. Usually Steam detects when a new folder is added to the library and integrates it in the client. Maybe you have to check in the settings that it uses Proton to launch the game.
Another option, but I have not tried that yet either, would be to backup the game from the Windows Steam client, and then restore it on Linux.