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I didn't. I kept both in two different but adjacent folders:

tales-from-the-unending-void-win-linux\TFTUV-0.9-Uncensored Edition (PC)

and

tales-from-the-unending-void-win-linux\TFTUV-0.10-Uncensored Edition (PC)

 I then ran the game from 0.10 and it managed to find the saves from 0.9. It seems to place new saves you then make in the 0.10 folder (game -> saves).

I haven't tried, but I think you can just move over the saves from 0.9 to 0.10 and then delete the entire 0.9 folder. 

The saves for any Renpy game are stored in the %appdata%/Renpy folders. even deleting you old file before downloading the new one shoudn't affect your saves. The new folder should automaticaly take the saves from there.