Mozy only backs up files physically stored on your machine or an attached hard drive; it cannot back up files that are stored online by other companies. If you were to store the files from your web based email to your machine by some method like running it through an installed Mail program such as Outlook, which saves the emails into a file on the hard drive, or export the emails to documents saved on your computer, then you could select them in Mozy and back them up.
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