I'm assuming that you are using internet email rather than Exchange (if exchange, you simply modify the person's name in the account settings and everything stored on the server will automatically show up on the new machine).
All of these will be stored in personal folders (.pst). Most people have only one pst, but be sure to look for an archive pst file or any other one they may have started. In Outlook, if you view Folder List, you'll see the top-level description (usually simply "Personal Folders"

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Do a search on the hard drive for *.pst. Default locations vary based on the operating system. Copy the pst file(s) to the new computer. When setting up outlook, point the location of the file to this pst file. This will move everything in that folder -- all emails, contacts, calendar, etc -- to the new computer. Don't forget to go to settings and put in his name and account information so that new emails flow in and out properly.
Once the new one is working, I'd make a backup and destroy the current email file. Most controllers wouldn't like their email to accidentally be "found" by a new user.
If you need to add a pst to an existing outlook setup, you can go to File, Open, and choose Outlook Data File or Personal Folders file (depending on your version of Outlook). Pretty straightforward!
Jennifer