I wondered if there is a way to export emails from Exchange 2010 accounts that mention a certain email address?
Do you mean export by To recipient or From sender name, perhaps CC recipient?
You can create a folder, then create a rule that will move or send a copy of those messages, meeting that criteria, into that folder, finally export just that folder.
No, OWA is not as robust as Outlook client.
So use Outlook?
Yes. You will really need to create and export from that rule in Outlook.
And it will move all mail sent or received from that specific email account?
When you export you are just making a copy so it will not be removed, they will be moved to that folder, since that is the idea.
Can I then export that folder?