broken lcd and screen

So I broke my screen and glass on my samsung galaxy s3 for verizon. Instead of just buying the lcd and screen by itself I was considering buying the front housing that already has everything together and it says just put in your motherboard. Basically it's just like the one on this link:

http://www.ebay.com/itm/130920526109?ssP...

But I wasn't sure if my motherboard would fit in one that says for sprint, u.s. cellular, etc. So I guess all I really need to know is will my motherboard from my phone work in any cases even if its from another carrier?