I got this issue...
Don't use the original app! indeed they increased the security verifications with 5.3 version.
Try to link your Facebook with the 5.2.2 mod, then update it with the 5.3 mod (when the game ask for it), without uninstall 5.2.2, and your save will be linked. It works, but forget the official app, it blocks the Facebook save for the mod users.