turmoil2750 In order to get push notifications, an app has to be running on the phone to keep a connection open with a server. Most Android phones have Google Play + Google Play Services installed to receive FCM messages. Facebook Messenger doesn't run in the background constantly and expects Google apps to be installed for push notifications to work.
If you need push notifications, you might consider installing Google Play in another profile along with Messenger and set up sending notifications to the current user from within that profile.