Here's how you do it:
- Start with a 1.1.1 or 1.1.2 jailbroken phone with Installer.app installed.
- Plug in your phone via USB to your computer.
- Download, extract, and run iBrickr Special 1.1.3 jailbreak edition (ibrickr.exe in the archive).
- iBrickr will determine what firmware you are running on your phone and make sure you can run the update.
- iBrickr will then guide you through the process of obtaining and modifying the 1.1.3 firmware (make sure to read everything thoroughly).
- iBrickr will upload the new firmware image to your phone. Note that this only puts the file on your phone and does not modify it at all, yet.
- When iBrickr finishes (should take about 10 minutes), it will tell you to go to Installer and install the "1.1.3 soft upgrade" package. Do that.
- When the installer finishes (this should take another 10-15 minutes), your phone should reboot with a fresh activated 1.1.3 firmware.