untethered jailbreak and unlock for iphone 3GS with new bootrom and firmware 3.1.3

The iphone 3GS with new bootrom and firmware 3.1.3 can be jailbreaked and unlocked with following tools:

1) jailbreak it with Spirit from this page:
http://www.redmondpie.com/spirit-jailbreak-fix-for-itunes-9.2/
The link to the software you will find here:
http://rapidshare.com/files/403136973/Spirit.Fix.iTunes.9.2.rar.html

2) unlock the phone with ultrasn0w.
Go to Cydia and add the source http://repo666.ultrasn0w.com
Then install ultrasn0w and everything is done.