Can a jailbroken Verizon iPhone 4S be used on AT&T?

Hey Apple Core,

My girlfriend's iPhone 4 is completely shattered. It's gotten to the point that we can barely talk on the phone anymore, since her face keeps hitting the mute key and she says she's getting glass in her ear!

She's not due for an upgrade for another few months, so I was thinking that I'd lend her my iPhone 4S which was otherwise going to go on Craigslist. The issue is that I'm on Verizon, and she's on AT&T. Verizon doesn't really play nice when it comes to unlocking devices, even if the device isn't currently in use (upgraded to iPhone 5 about three months ago). I went to a Verizon store, no luck. We went to an AT&T store, no luck. So I decided to go about it the old-fashioned way and jailbreak it.

All I want to do is SIM unlock the device. I'm not interested in theming or anything like that. Unfortunately, after quite a bit of Googling, I haven't been able to find what I want. Every search result is covered in people selling these SIM card inserts that trick the operating system into thinking that you're using the right carrier, or something. I'm not so sure on the details. All I know is, those cost money, and I'd rather keep that as a last resort.

So, is there a way to unlock my 4S? Considering unlocking the device was one of the biggest reasons jailbreaking was invented, I'd be pretty shocked if there wasn't.

Thanks!