Transfer iOS app data to a different account

I have an iPad 2 currently using my AppleID. I want to reset it (almost) completely and change it to my girlfriend's Apple ID.

The thing is: there are 2 or 3 apps whose data we really don't want to loose. They are free apps, so it's trivial to reinstall them under the new account.

I only need a way of backing up the data of these apps under my Apple ID and then restoring it under her Apple ID.

Is there a way to achieve this?

I'm not trying to transfer purchases or anything like that, just copy some data.

NOTE: The software needs to be Windows or Linux.

You can backup data from apps with a program such as PhoneView (Mac) or iFunBox (Mac & Windows).

Browse, manage and download most any data saved by App Store apps from your iPhone, iPad or iPod Touch. If you're looking for a quick way to download saved recordings, videos or images from your apps, this is it. Even transfer game high scores between devices. --PhoneView

This data can then be restored to a new installation of an app under a different Apple ID or even on a different device.

Extending @grgarside's answer:

1. Acquire iTools, iFunbox, and a Windows or Mac desktop computer
2. Use iTools to backup the apps to desktop
3. Uninstall all apps
4. change AppleID for App store, iCloud, etc. everywhere on device
5. Power off/on cycle
6. Reinstall the apps from App store (not from backup!)
7. On desktop computer, unzip the .ipa files to a staging area
8. With iFunbox, for each application:
   • Manage Files and
   • copy Documents and Library from {desktop}\staging_area\{app name}\Container\ to {i-thing]\User Applications\{app name}\ ...and you should be good to go.

Notes:

Strictly speaking, you should be able to use iFunbox for everything. However it crashed frequently on my Win7 system so I'm not inclined to use it more than necessary.

.ipa files are just zip archives with a different extension. You may need to rename .zip in order to extract the contents.

The reason for #3 and #6 is that the appleid is welded into the app before it is downloaded and installed. For the same reason we don't use either management app's native restore mechanism.

If the device is jailbroken you might be able to use iTools for the whole process. (On the unbroken ipad I was using the iTools file system view did not show the User Application data.)

This recipe worked for the half dozen apps I needed to move, but I expect some apps have a more complicated process, e.g. copy X,Y,Z from Documents, but leave behind T,U,V and edit the headers in W,X to the new account into.