The following PowerShell snippet can be used to to export the results of a message trace, unfortunately at the time of writing the Office365 portal does not allow you to do this in the GUI.

Capture

Connecting to Office365 via Powershell

Exporting messages based on the sender address

Note the dates and in the American format mm/dd/yy

Exporting messages based on the recipient address

Note the dates and in the American format mm/dd/yy