If a user is receiving email in their Outlook on the web mailbox but not on the email app that's installed on their machine, that could indicate that there's an issue with the users machine or email app. Use Outlook on the web to look for missing messages - 5 minutes Have the affected user try the following solutions before you move on to admin-specific tasks.
If only one user is reporting having trouble receiving email, there might be a problem with their email account or their email app. First things first, check if there's a problem with Outlook or another email app Is something wrong with Outlook? Is the Office 365 service down? Is there a problem with mail flow or spam filter settings? Or is the problem due to something that's outside your control, like the sender is on a global block list? Fortunately, Office 365 provides powerful automated tools that can help you find and fix a variety of problems.
You might run through several troubleshooting scenarios in your mind. When users report that they aren't getting email, it can be hard to find what's wrong. Find and fix email delivery issues as an Office 365 for business admin