I passed level 365, but it doesn't let me move ahead on the phone. Works fine on computer.
Update your game on the phone to the latest version. The sync is done via facebook. It should sync automatically, if it does not sync, restart the game and make sure your internet is working.
If you get the wrench symbol on the phone, that means the version of the game on your phone is limited to that level, usually updating the game will let you play more levels.
The newest version of the game should definitely let you move pass level 365.