Yes, she can but it's not elegant.
Simply set up the mail account on both PCs. Tell OE not to delete the mail from the server on either machine for two days (or any time limit you want).
Then all incoming mail will be available on both.
If she wants a record of outgoing mail on both machines, set the account to BCC herself.
As I say, it's not elegant, but it will work.
Synchronisation of mail is not easy - Thunderbird will do it better if she is interested in changing mail programs.