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This guide assumes you have SSH installed on your jailbroken iPhone running 1.1.1 firmware. If you don't, the following guides will get you up to speed:

Dev Team Jailbreak 1.1.1 from 1.0.2 Windows

Dev Team Installing SSH 1.1.1 Windows

It is also necessary to install BSD World and Springpatch by following these guides:

Dev Team Install BSD World 1.1.1 Windows

Dev Team Install Springpatch 1.1.1 Windows

Step 1

Download and extract the following package to anywhere: AppTapp Installer.app packaged for manual install via SSH

Note: Using this package (following this guide) modifies M68AP.plist and may hide icons for other third-party applications you may have installed manually.

Step 2

Download and open WinSCP: Available here!

Connect to your iPhone.

IP Address: Check your current WiFi settings on your iPhone.
(If you have trouble, try issuing a static IP.)
Login Name: root
Password: alpine
Connection Type: SCP
Port: 22

Step 3

Navigate to the root directory of your iPhone (the / directory, not /var/root/ or /private/var/root).

Drag-and-drop the extracted contents of the package (the Applications and System directories) to the root directory of your iPhone. Before pressing the Copy button, press More >> to reveal more options. Check the box next to "Set permissions" and make sure the textbox has this text:

rwxr-xr-x

When you're done it should look something like this:

Once your options look similar, press the Copy button. Note, if prompted to overwrite, select Yes to All. Nothing will be overwritten, the contents of /Applications/ and /System/ will just be merged with their corresponding directories on your iPhone.

Congratulations!

That's it!! After a reboot, the Installer icon should appear on your SpringBoard. The package is made so that it not only installs AppTapp Installer, but also places the icon on the homescreen. Note that this re-arranging may result in the loss of icons on your homescreen for any other third-party apps you may have already installed. From here on out any third-party application added through AppTapp Installer should automatically place its icon on the homescreen for you. To add the Contacts Application icon to your homescreen, check out this guide: Dev Team Show Contacts App 1.1.1 Windows