You can use adb backup. You can specify the package name for backup a single app.
adb backup [-f <file>] [-apk|-noapk] [-obb|-noobb] [-shared|-noshared] [-all] [-system|nosystem] [-keyvalue|-nokeyvalue] [<packages...>]
adb restore <file>
Note: some apps won't allow adb backup. even if adb backup is allowed, cache is not included.
Ok. I eventually got my SMS back. But if someone is searching for an answer, here is my solution that, I hope, will help.
I guessed the problem came from the android version. So, basically, I did the following:
1. Grap your old phone under Android 4.0.4 (you can use someone else's phone, just make sure to backup their messages before you do anything. To be ...