Can I use the nano sim card of iPhone 5C for an iPhone 4S?

My grandmother has been thinking of buying an iPhone 5C (because she saw a good deal) and she wants to give it to me and use her old iPhone 4S. The problem is that she wants to use the nano sim card of the 5C for her 4S in order to save her phone number that she will receive once she buys the phone. Is it possible for a 4S to work with the sim card of a 5C?