iOS6.1.3

I'm currently on iOS 5.0.1 on my iPhone 4s, and want to upgrade. The upgrade available for me through iTunes is to iOS6.1.3. The evasi0n jailbreak says it works for iOS6.0 to 6.1.2. I'm assuming this means it wouldn't work if I upgraded to 6.1.3, so is there a way I can upgrade just to 6.1.2?

edit: I found this. Can I just download it, and through iTunes, use this to update?