Upgrading your iTouch or iPhone’s firmware from 1.1.2 to 1.1.3 is easy, thanks to the jailbreak team’s easy upgrade installer.
Open your installer.app and make sure that it’s version 3. If it’s not, upgrade it first. Once done, go to the sources icon, tap any source item in your list and tap on the add button on the top right. Add this link, http://www.touchrepo.com/repo.xml
Go to the install icon below and tap on it. Look for the iphone packages and select 1.1.3
Exit installer.app and look for the apple icon with prison bars behind it broken. Tap on that icon and let it do the rest for you (downloading the package, decompressing and installing). Automatic reboot will take place after installation is done and your firmware version will then be 1.1.3. Make sure your wifi connection is on or else it wont download the package upgrade installer.
Note: Be patient when the installer upgrades itself. it may take awhile. And makre sure you back up all your source list as the upgrade cleans everything including your installed 3rd party apps.