If your friend (cough, you, cough ) can gain access to her old email address, email contact@Groundspeak.com and the fabulous ladies and gentlemen would be happy to send the password reminder. If that's not an option, then yes, just like you suggested, she can sign up for a new free account at this page:
http://www.geocaching.com/login/new.aspx
She is welcome to re-log her finds under the new account, as long as she indicates as such in the logs.
Happy caching!