is there anyone know how to install older version of apk on to newer version of apk already installed, and without rooting and patching system with Lucky Patcher, uninstalling newer version.

This may be a weird question. I'm having the situation that I want to root Sharp SH-06E firmware 1.00.08

 http://worldtsunami.blog136.fc2.com/blog-entry-52.html

Firmware newer than 1.00.07 has new root protection. This new root protection involved preventing installation of hacked VpnFaker.apk to data partition. Hacked VpnFaker is required for rooting process. The blog says that root is possible if VpnFaker is already installed (used to root on firmware older than 1.00.08), but VpnFaker in data partition on my phone is removed during firmware update. (I was on 1.00.01, root, then unroot to update firmware)

Sharp has a lot of root protection, even on firmware older than 1.00.08, rooting process use workaround that mounts system image file in data partition on boot instead of directly writing file to system partition.

VpnFaker is indeed VpnDialogs of Android System 4.0.4, while newer version installed in system partition is version 4.2.2-1.00.08.

So, is there a way to sign 4.0.4 VpnFaker to has same signature as 4.2.2 VpnDialogs. Here is the link to the files http://forum.xda-developers.com/showthread.php?t=2760470

Is it possible to install an older version of an app (via .apk), when a newer version is already installed on the device ­– without rooting and patching system with Lucky Patcher or previously uninstalling the newer version?

Some background

This may be a weird question. I'm having the situation that I want to root Sharp SH-06E firmware 1.00.08, as described in this blog post.

Firmware newer than 1.00.07 has new root protection. This new root protection involved preventing installation of hacked VpnFaker.apk to data partition. Hacked VpnFaker is required for rooting process. The blog says that root is possible if VpnFaker is already installed (used to root on firmware older than 1.00.08), but VpnFaker in data partition on my phone is removed during firmware update. (I was on 1.00.01, root, then unroot to update firmware)

Sharp has a lot of root protection, even on firmware older than 1.00.08, the rooting process uses a workaround that mounts system image file in data partition on boot instead of directly writing file to system partition.

VpnFaker is indeed VpnDialogs of Android System 4.0.4, while newer version installed in system partition is version 4.2.2-1.00.08.

Final question

So, is there a way to sign 4.0.4 VpnFaker to have the same signature as 4.2.2 VpnDialogs. Here is the link to the files.