Game saves for Frozen Free Fall and Angry Birds 2

[AC Question]

Hello.

I've upgraded my phone from the LG G3 to the Sony Xperia XZ. If possible, I want to move my game progress for Frozen Free Fall and Angry Birds 2 onto my new device.

However, despite logging into Google Play Services successfully, I can't seem to transfer the progress.

Any idea how I might go about doing this? Many thanks.