While restoring e-mails or any other part of the mailbox into an original mailbox, you could unintentionally create "doubles" of the same items.
To avoid this, you can use the redirection option in your backup program. (I'm using Backup Exec.) Use this to redirect restore to a different mailbox, specifically created for this purpose.
For example "restore". Now give the user permission to view "restore" mailbox through Exchange Admin and add it to user's profile through Control Panel/Mail.
Your user will be able to see both mailboxes at once and move the needed items. After the user is done, empty the mailbox using Clean Mailbox option in Exchange Admin. It is ready for another use.