When you attempt to move mailbox from/to Exchange Online, you receive the error:
The call to 'net.tcp://server name/Microsoft.Exchange.MailboxReplicationService server name' timed out. Error details: This request operation sent to net.tcp:// server name//Microsoft.Exchange.MailboxReplicationService did not receive a reply within the configured timeout (00:01:00). The time allotted to this operation may have been a portion of a longer timeout. This may be because the service is still processing the operation or because the service was unable to send a reply message. Please consider increasing the operation timeout (by casting the channel/proxy to IContextChannel and setting the OperationTimeout property) and ensure that the service is able to connect to the client.
The DataImportTimeout property may be set too low.
To isolate the issue, you may check how it works if you increase the timeout with the following steps:
<!-- Mailbox Replication Proxy Server configuration -->
More information and documentations for your reference:
Troubleshooting Mailbox Moves