If you started playing Family Guy: The Quest for Stuff on Facebook, you can switch to your mobile device at any time and pick up right where you left off.
To do that, you must first download the app and start a new game. Play through the tutorial, and tap the Main Menu screen once it appears.
From there, tap Account Info, followed by Connect with Facebook.
A screen will pop up offering to load your game. You'll see your name and level to confirm it's the one you want. Tap Link, followed by Continue.
You're all set! You can switch between playing on Facebook and mobile, and even between iOS, Android and Amazon, at any time.