It wouldn't keep the credentials because you need to setup the HP Mini to sign in with the user account as was setup on the Linkstation Live on XP itself. Access XP's user account and create a username for her with the password and then on the LS Live create the same username and password and assign drive priviledges for her. After the user account is created, map the drive and enable save log-in. When she restarts her HP Mini, an XP log in screen will be presented. Select the username and then enter the password and when the machine finishes booting up to the desktop, those mapped drives will be available just like a regular drive.
Hope this helps.