This system does not allow you to do this conveniently, so you need to first copy your save from the game's save folder to another folder on the device, then delete the old version, install the new version, then run the game for the first time to create a save folder, then copy your save to it.
This is a feature of the Android system.
The save folder is located somewhere here: Phone\Android\data\www.townofmagic.com\files\saves
And make sure that in your save, Celica woke up in the morning. This will increase the chance of normal progress saving when changing the game version to about 100%.