If you have a wireless network connection there's a great post on here that tells you how to upgrade directly from 1.1.1 to 1.1.3 without going through 1.1.2 at all. It's much easier, takes a bit a time but pretty much hassle free. I followed this myself with no problems so try it and see for yourself. Remember before you start the actual jailbreak to make sure that you change your autolock to never under the setting menu option so that it doesn't shut down half way through the process. Takes about 4-5 hours. The post is here
https://forums.macrumors.com/threads/427812/
Cheers!