IPhone: Transferring App Data not on App Store?

Can some iOS masters help me transfer app data from an app to a new phone?

The normal backup and restore from backup method works fine with all apps that were still on the app store. Right now when I try to restore it, it just says "Unable To Install '… ' The app is no longer available in the App Store."

Get an Android!

Use iTunes to back up the old phone and restore it to the new phone.

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