JMP shares the Recent Files list across JMP versions and they are stored per-user under this key:
Computer\HKEY_CURRENT_USER\SOFTWARE\SAS Institute Inc.\JMP\Recent\Files
Here is a picture from my machine. Be sure you check the registry when logged in as her userid since they are stored in HKEY_CURRENT_USER and the userid matters.
So you ought to be able to login to the old PC as her userid, run regedit and rigt-click Export on the "Files" folder (if you can find it). And have her import the file into her new machine.
John