Office 365 Mail Flow Troubleshooter
The Office 365 Support team has just released a guided mail flow troubleshooter here:
If you have users complaining that mail delivery takes too long, or that mails are remaining in their outbox, or that recipients are not receiving e-mails at all; the guided walkthrough will step you through the troubleshooting steps required to diagnose and resolve the problem
Access the troubleshooter here: https://aka.ms/mailflow
For your reference, the following diagram shows many of the components involved with mail delivery from sender to receiver, any of which could be interfering with your email arriving:
