as a matter of fact there are too many tutorials for updating to 1.1.3 but most of them sucks,Nate true’s method is easy and fast but very buggy and NOT RECOMMENDED.

i personally followed iClarified tutorial but i don’t do it, it’s too risky and will brick your iPhone,but it’s restorable fortunately.while soft jailbreak didn’t upgrade basband you can easily downgrade like before

but my tutorial is about to begin:

First you need these:

1. fully unlocked an jailbroken 1.1.2 (if you need tutorial here is for Mac and this is for PC)
2. a wifi connection
3. iPhone 1.1.3 firmware (if you did upgrade using iBrickr you must have it 1.1.3.ipsw in iBrickr folder)
4. installer.app
5. WinSCP

step 1:goto installer and install BSD subsystem 2.0

step 2:update installer (make user you refreshed sources and your installer.app is up to date)

step 3:install Official 1.1.3 upgrader

TIP: if you don’t have fast wifi connection you can manually download 1.1.3 firmware and copy it by WicSCP to /var/root/Media

step 4:quit installer and run upgrade