Emails being stored on the network may mean that is where he stores his pst file. We do that at my work place. No important files are stored locally, so when there is hardware failure or any other problem, we can either reimage it and reload outlook w/o backing up info or just give the person a new machine.
The same can be done with Eudora.
Anyway, to answer the person's question, just back up the pst file. Your address book, tasks, calendar, and email will all be in there. There are several ways to restore it, so check up on that too.