Sign in to the Facebook profile you want to connect to on the Facebook mobile app and load Family Guy: The Quest for Stuff on your device.

Go to Menu > Account Info and write down the 32-digit code in the bottom left corner of the screen. This is your Player ID.

Tap the blue "Delete Facebook" button in the upper left. You will receive a warning that this will disconnect your game from your Facebook profile.

Once you've disconnected the game, tap the button again. This will connect it to the new Facebook account.