Symptom:

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.

Cause:

The DataImportTimeout property may be set too low.

Resolution:

To isolate the issue, you may check how it works if you increase the timeout with the following steps:

1. On the Client Access server, open the following file with a text editor such as Notepad:

\ExchWeb\EWS\web.config

1. Locate the following section in the web.config file:

<!-- Mailbox Replication Proxy Server configuration -->

<MRSProxyConfiguration

IsEnabled="true"

MaxMRSConnections="100"

DataImportTimeout="00:01:00" />

1. Make sure value of the IsEnabled property is set to true.
2. Check the value of the DataImportTimeout property. The minimum value is one minute (00:01:00), and the maximum value is 30 minutes (00:30:00).
3. Set a higher value, but make sure the value is less than 30 minutes.
4. The recommended value for this field should be 00:20:00 (20 minutes).
5. After the values are configured correctly, save and close the web.config file.

More information and documentations for your reference:

Troubleshooting Mailbox Moves

http://64.4.11.252/en-us/library/dd638094.aspx