Here is a really good article on how to migrate Mozy over to the Mac. Note that part of this is deleting the files from our servers if you want to use the same computer slot on the account. If you do that, just make sure all the files are on the new computer first!
To resume backups, please follow steps as per http://support.mozy.com/articles/en_US/FAQ/How-do-I-migrate-from-Windows-to-Mac to delete the Windows computer from the account so you can install Mozy to add the Mac for backups. The restore will need to be complete before you delete the Windows computer. Once a computer is deleted from the account, so are all the backed up files. But when switching platforms, this needs to be done.
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