Search is broken for a user’s mailbox in both the Outlook desktop application and in Outlook Web Access.
The recommended solution is to move the mailbox in Exchange Online.
New-MoveRequest Tony@StarkEnterprises.com
You monitor the status of this request using this command.
Get-MoveRequestStatistics -Identity Tony@StartEnterprises.com
This process will take time. My experience is that a 40GB mailbox can take up to 10 hours to complete.
Looking for a solution to “no search results in Outlook”, I found this article.