MacOS – Restore files from Time Machine to a different Mac

Your best bet is to turn off Time Machine, eject the backup drive and get some help from someone trained to know what Time Machine looks like.

It's entirely possible, the software deleted the old files and over-wrote them with new backups. It's also possible you had a minor glitch in the permissions and all is well.

Assuming you are near a retail store, you can usually get a quick read from someone in the store or worst case, make a support request at the bar. Phone support is also an option, but I've found that taking the backup drive and the mac (as well as your old mac drive / CPU) in to the store is the fastest way to get someone seeing exactly what is going on and your data uncertainty sorted.

As much as I like to help guide people, it's really best to disconnect the drives and reduce the risk of more files getting deleted and not learn on this one instance if you can get some professional help on this.

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.