These are instructions on how to unlock your iPhone using SAM. This method will work with the iPhone 4S, iPhone 4, iPhone 3GS, and iPhone 3G on any jailbreakable firmware including 5.x.
If you want to view the step by step instructions click here.
If push notifications stop after this process, you can restore then with the Clear Push utility in SAM, followed by connecting to iTunes.
Your phone will work normally with your SIM card and that SIM card ONLY since we have tricked iTunes to think that ICCID is one of the intended carrier's. The phone can be rebooted and connected to iTunes freely without losing the "unlock", at least for now.
A big thanks to Loktar_Sun and Laforet for their contributions!