itch.io

I'm not too familiar with how phone file explorers work, so this is mostly a guess. Using a file explorer, you should be able to transfer save files into the downloaded update .apk file.

You should be able to just update the app (download it first, then install it to replace the old one). 

But if you have errors or troubles, you can export your save files by pressing buttons Export save and Export profile on Load screen.

After that you can just delete the game and install the new update, then import the save files back.