After you move a mailbox from the on-premises Microsoft Exchange Server environment to Microsoft Exchange Online in Microsoft Office 365 in a hybrid deployment, you receive the following warning message:
A replication delay in the service occurred. This may prevent some post-migration cleanup tasks from taking effect immediately.
The user may be unable to access his or her mailbox immediately after the migration is complete. As soon as replication is complete, the user will be able to access his or her mailbox. If the user continues to be unable to access his or her mailbox 60 minutes after the migration is complete, contact Office 365 Support.