What I did was:
1.- Log off from the Facebook App. (Uninstall of you want).
2.- Delete Facebook informaci?n from Email-Account settings.
3.- Block everything on the Background tasks
4.- Do a soft reset
5.- Reboot the Phone normally (turning off and turning on).
6.- Reinstall Facebook Messenger App (you might want to do this on the first step)
7.- Log-in and you should be able to use Messenger with notifications working properly.
8.- Then you can turn-on the background taskt (no more than 6) and install the rest.
That's how I got my app to work.