Information: The Export-Mailbox cmdlet exports all message types, including messages, calendar items, contacts, distribution lists, journal entries, tasks, notes, and documents. However, the Export-Mailbox cmdlet does not export rules.
To export data from a .PST file, you must run the Export-Mailbox cmdlet on a 32-bit computer that has the 32-bit version of the Exchange management tools and Outlook 2003 Service Pack 2 (SP2) or Outlook 2007 installed.
Please be aware that there are prerequisites to exporting mailboxes. You need a location to export the mailbox to along with permissions set on the mailbox.
In the example below I will show you how:
First add permission to the users mailbox
Add-MailboxPermission -identity user –Accessrights FULLACCESS -User admin
Now we export the mailbox
Export-Mailbox -identity user -PSTFolderPath c:user.pst
Now you should be safe to remove the email boxes and free up space