We had an interesting issue where user’s mailbox was migrated to Office 365 but he could not see any new mail in the mailbox. Even sending himself mail did not show the new e-mail items.
We sent a few test mails and tracked the mail from on premises Exchange to Office 365 which showed that the mail delivered to the cloud.
We then traced the mail items from within the Office 365 admin portal and confirmed that the mails delivered to the mailbox but we could still not see the items.
Thinking that it might be desktop related we asked the user to logon to Outlook Web App and we could still not find the mail items that showed as being delivered to the mailbox.
I then ran the Get-InboxRule cmdlet against the mailbox to see if a rule might be interfering. Suddenly the new test mails sent after I ran the cmdlet delivered to the mailbox and we were able to see them. Testing all new mail to and from the mailbox seemed to have worked after I ran the Get-InboxRule cmdlet as if it reset the rules somehow.
This still boggles my mind but it’s worth a try if you have the same issue.