I heard from Sprint when I called today that they're not allowing the transfer of iPhone 5's like what you are trying to do since I am trying to do the same thing with my Mother's upgrade. Does anyone have any confirmation on this or if they've been able to transfer the phone number? I can't seem to find anything saying otherwise on the Sprint website.
It's called a line swap and they will do it. You have to first activate the iPhone 5 on your mother's line. Then call technical support and tell them you want to swap the iPhone to your line and swap her back to her original handset. It takes about 15 minutes. You have to have both phones in front of you and turned OFF when you call from a land line to get this done.