Default [Q] Checksum Error on restoring userdata*****.backup file

As my android 4.2.1 phone has a broken / non-functional screen after dropping heavily on floor, I enter recovery mode (Android System Recovery 3e) and select "backup user data" to generate a whole system backup file in the format of userdata*****.backup.

Then I purchase a brand new phone of same model but this backup file cannot be restored. It comes up with a "Checksum error". Something weird, I also try to restore the same file to the broken phone and it works with no error. It seems that backup file can only be applied to the original phone but not the other even of same model. Is it true?

Note that the broken phone has NO "USB debugging" mode enabled and obviously I cannot activate debugging with a broken screen. It means that it is the only way I can create a whole system backup.

My question is, as I have many important messages history / contacts, how do I read / extract the backup file? or the best of all restore it to another phone? Any help is much appreciated.