First, make sure you save in the Town square, then you copy the saves folder (located in the game one) to the new version. This applies to the PC version, I don't know how things work on Android.
EDIT: Ah! Once you're on the new version, remember to go into options and update your save.
I've been playing the game for over a year now and if you hadn't said there was a save update feature in the settings. I wouldn't even notice. Thanks for the information :)