Jailbreaking Apple TV 2 with iOS 5.1 Question

I have an Apple TV 2 that is jailbroken using Season Pass and is currently running software version 5.0.1 with FireCore’s ATV Flash Black.

 

I also have the opportunity to acquire another Apple TV 2 that is running software version 5.1 in exchange for an Apple TV 3.

 

Is there a way to jailbreak the one running version 5.1?  Can I restore it from the IPSW file that was saved when I jailbroke the other Apple TV 2 or does the device signature prevent me from applying that file to a different Apple TV?

 

Please provide or point me at instructions that might accomplish this.