We have been migrating mailboxes from on-prem Exchange 2010 to O365. All was good except two mailboxes. After migration was successful, these two mailboxes did not move to 'disconnected mailbox' status as they should be. Therefore, all external emails and O365 went to O365 that users can view them in OWA and on-prem emails went to their Outlook because Outlook is connected to on-prem Exchange automatically instead of O365.
Solution: (by Awesome MS support)
1. Disable the mailbox in Exchange Management Console on Exchange 2010 or use the command below. My case I use GUI.
Disable-Mailbox -identity -<user_identity_email>
2. Issue the next command
Enable-RemoteMailbox "<user_identity_email>" -RemoteRoutingAddress "<email@example.com>"
3. Run a Azure delta sync - (or full sync)
Start-ADSyncSyncCycle -PolicyType Delta
Start-ADSyncSyncCycle -PolicyType Initial
4. Create a new Outlook profile which should connect to O365.