Please refer to the following article: https://blogs.technet.microsoft.com/asiasupp/2011/06/23/when-you-attempt-to-move-mailbox-fromto-exchange-online-you-receive-the-error-the-call-to-microsoft-exchange-mailboxreplicationservice-timed-out/
I hope this helps!
If an Answer is helpful, please click "Accept Answer" and upvote it.
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.