Save data is saved using Unity's PlayerPrefs. For Windows, PlayerPrefs is stored in the registry. I'm not sure where it's saved on the Linux player. You could definitely pull it over by-hand but we don't have an easy way to do it, sorry.
On Linux, the preferences are saved in $HOME/.config/unity3d/Variety is Hope/VineWorlds/ and it looks like the preferences are available in plain XML in the prefs file in that directory. So you can export the registry entries as a .reg file, then open and compare both in a text editor and change the properties in the prefs XML accordingly.