Let's upgrade the unlocked iPhone from firmware 2.2 to 2.2.1.
Inventory and backup
Install AptBackup. Run it and tap Backup. Wow, that was easy.
In iTunes, on your device's Summary tab, in the Version section, click Update. I previously let iTunes download firmware 2.2.1, but I didn't install it. iTunes attempts to make its own backup of your contacts, calendar, and so on, but then complains that it can't--this is a consequence of your having previously jailbreaked the iPhone. Wait a few minutes while iTunes installs firmware 2.1. iTunes reports that it's done, and the phone reboots. iTunes notices the iPhone and reports that an incompatible SIM is installed. Time to jailbreak and unlock
Jailbreak and unlock
I download QuickPwn 2.2.5 and the two bootloader files from iPhone Hacks. I install and run QuickPwn. I play nice, following the instruction, and the iPhone is back up and running in a few more minutes.
Restore Cydia apps
In Cydia, install AptBackup. Run it and tap Restore. Wow, that was easy.