Sprint iPhone 4s chipset into Verizon iPhone 4s phone

My Iphone 4s is on the Sprint Network. It got wet, broke the screen. I'm replacing it, but I just got a Verizon Iphone 4s for free. I'm assuming, if my chipset is good, I can put it in the Verizon one and I should be good to go? Any issues anyone can think of. Then I'll put together the other phone at my leisure and not feel pressured.

Edit: I'll also add, the Verizon phone is a clean phone. I am getting it from my Step Dad, that upgraded to an Iphone 5.