3gs 3.1.2 Restore from backup of 3.1.3 3g

[marcus5]

I am currently using a 3g 3.1.3 but I just bought a 3gs with 3.1.2 firmware hoping to jailbreak it. I use at&t so I don't need to unlock it, just jailbreak it. I was hoping that I would be able to jailbreak the new one AND backup the old one to itunes then transfer all of my contacts and pictures and text conversations and everything from the backup of the 3g to the new jailbroken 3gs. Is this possible?