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The Administrator can control users, groups and certain other features which manage the mailboxes of its users. In this scenario, the administrator goes to Reporting then Mailbox Searches, a feature which is built into Exchange Online and other versions of Exchange Server. This allows the administrator to search for certain text in any mailboxes across the organisation, or to wildcard search across any number of users' folders.
Colour key for viewers: Red border is the administrator's email view. Green border is the student user's email view. Blue border is the administrator's console.
For more background on this screenshot gallery, head over to the iGeneration blog which explains all.