If your daughter is using 'POP3' mail, the default setting on Outlook is for mail to be deleted from the server as soon as one computer accesses it. Your daughter will need to change the setting, so that the mail is held on the server for a sufficient length of time to allow the other computer to also collect it.
These instructions are actually for Outlook Express but Outlook usually does things the same way:
Open Outlook
Click Tools, Accounts, Mail
Click on the name of the mail account, then on Properties and Advanced.
In the 'Delivery' field place a tick alongside 'Leave a copy of message on server'
Choose a suitable time interval.
Click Apply, OK and Close.
Repeat on the other computer.
Chris