Updating jailbroken iPhone 4s iOS 5.1.1 to 6.1.3 help needed?

Full story:

I bought my iPhone off a friend, who previously got it on bill pay, but stopped paying the bill, so they disabled the phone.
He got the phone jailbroken to bypass that, and now the phone is working properly, pay-as-you-go, but it is jailbroken.

The phone will NOT work without being jailbroken.

I was wondering how do I update it from iOS 5.1.1 to iOS 6.1.3? (Keeping in mind it NEEDS to be jailbroken to work)

No it won't work without cell service btw ios 5 and 6 are not that different

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