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:
fully unlocked an jailbroken 1.1.2 (if you need tutorial here is for Mac and this is for PC)