If you want to connect your game to  another Facebook account, please follow these steps:

1. Link the game to Google/Game Center (main menu - settings - accounts)
2. Delete the game
3. Log in to the correct Account in the Facebook application
4. Download the game
5. Upload progress from Google/Game Center
6. Link the game to the correct Facebook account. (main menu - settings - accounts - Facebook - type login/password of your Facebook account)

Please, note that the "Main menu - Facebook" option doesn't link your game to Facebook. Such an option just downloads the list of your friends from your Facebook account (so that you can see your friends from Facebook who also plays the game), but the game remains unlinked.

If you want to link the game to another Google/Game Center address, you need to follow these steps:

1. Link your game to Facebook (main menu - settings - accounts)
2. Delete the game
3. Log out your old Google/Came Center account everywhere: store, device settings
4. Log in to your new Account everywhere
5. Download the game
6. Settings - accounts - Facebook. Load your game
7. Settings - accounts - Google Play/Game Center, link your game to new Account