[Q] Transferring App Data from Xperia Neo (MT15i)

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http://forum.xda-developers.com – I am currently using a non-rooted Xperia Neo (M15i) on 4.0.4 4.1.B.0.587, and am planning to change my phone (to Xperia Z). I would like to transfer some app data for a game (Puzzle & Dragons) to it. However the app does not run on rooted phones. I have tried to use adb backup but I do not see the prompt screen to provide a password on my phone, and I get an empty .ab file instead. I have also tried apps like Carbon and Ultimate Backup Tool also to no avail... I have read through numerous threads on this forum about how to root my Xperia Neo and to use Titanium Backup, but I am not (HowTos)