Can I put a 4g SIM card in a AT&T iphone 5?

My mom has the iphone 5 and she wants to give it to me. So I'm wondering if we could just which SIM cards. We're both under contract so we want to do this secretly and can a 4g lte sim go in a iphone 4s. I'm going to cut it and get a adapter if so.

The 4s is not compatible in the 4s network, so the short answer is no. Internal components are not the same in 4s as they are in the iPhone 5. Once works off hspa+ network and the 5 runs on 4glte. Just have the store give you a new SIM card for the 4s, which AT&T brands 4g, not lte though, which is equivalent to Verizon's 3G network.