How to restore time machine backup to a new machine running a different version of the Mac OS?
In the Applications directory, there is a subdirectory called Utilities. In Utilities you'll find Migration Assistant. Or just use spotlight to launch it.

Migration Assistant has the option to restore from another machine, a Time Machine Backup, or another disk.

Make sure the TM disk is plugged in to your wife's new machine, and you should be able to select it from a list of volumes.