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On windows, you can use the "update files only".zip when you have the previous version. It contains all files that were changed since the last update. (Caution: Skipping updated when using the update files means that you'll be missing files! Only use the update files when you have the previous public release)
A second option is to re-download the full game and move the saves from the www/save folder of the old game version to the same folder in the new game folder.

I'm showing both option in this video:

Updates are always made save file compatible.

Thank you for the clarifications and guide.