I realize that you don't want to restore the iPad backup, but you can restore an iPad backup to an iPhone as long as the backup does not have a newer iOS tied to it than the phone has on it. If the phone has an older iOS, it would have to be updated to the newre iOS first.
Having said that, you can back up the phone to her computer. Without connecting the phone, Launch iTunes and go to Edit>Preferences>Devices (Windows) or ITunes>Preferences>Devices (Mac). Select the option at the bottom where it says Prevent iPods, iPad and iPhones from Syncing automatically. Click OK. Quit iTunes. That prevents auto syncing of all iOS devices.
Now connect the phone to the computer again, launch iTunes, select the phone from the devices icon at the top and click on Backup Now. After the backup completes go to File>Devices>Transfer purchases>iPhone Name. This will transfer all purchase except apps, into her iTunes library. Apps can be downloaded again if needed and you can restore the backup after apps are downloaded which will restore all app data.
Take a look at these before you go further.
Syncing to a "New" Computer or replacing a "crashed" Hard Drive
How to back up your iPhone, iPad, and iPod touch - Apple Support
Redownload or transfer your iTunes Store purchases from an iPhone, iPad, or iPod to a computer - Apple Support