Need help for In-app integration of Google cloud-messaging for notification/message

Hello,
We have developed separate android app for mobile version of a community.
We are using "Google cloud-messaging" to push community notification/message to the mobile app.
Reference - https://firebase.google.com/docs/cloud-messaging/https://firebase.google.com/docs/cloud-messaging/

Push notification to the app are working in below 2 cases :-
1. when app is running in foreground
1. when app is running in background

Consider below scenario :-
1. user A is logged in into Desktop community.
2. user A send message to user B (who is offline)
3. user B logs into mobile app
Issue :-
Though user B is logged into mobile app now, he does not receive the message/notification which was sent previously (i.e. while user B was offline)

Is there any way to handle this scenario?
Is there any way Lithium can handle/integrate such push server (in our case for Notes API) so that other third-party applications can get messages/notifications real-time experience?

Thanks,

Vaishnavi