Make sure all apps show Connected status.
If you transferred your purchases/apps from your old device to your new device (i.e. restoring new phone from old phone backup) - please, uninstall GG app on one of those devices and install a new copy from the AppStore.
Thus you'll replace an identical copy of GG app by the app with new ID. And sync feature will restore its functionality.
Choose "Use group data" when prompted if current app has less data than your Group.
* Make sure you download same version (Free/Basic/Pro) as was installed before. If you upgraded to Pro by in-app purchase from Basic version - repeat same process, as purchasing Pro directly will result in extra charge from Apple.