Is it possible to replace an entire phone? Full Refurbish?

I know this is a very odd question, but I have 2 iPhone 5s that are both gold. One of the phones has an activation lock on it and I have been unable to contact the original owner, he left for Australia a month ago and has changed contact information/doesn't care to be reached by anyone; but that aside. The other phone is about a year old and has gone through a lot, the front glass is completely destroyed, the back is scratched badly and the chassis is dented in spots. It also perform's pretty badly. It freezes and I have to hard restart it a lot.

So here's my question, is there a way to transplant the phone and storage part of my 64gb phone into the body of the 16gb iPhone? Or is this more work then worth it? At the end of the day I think it would leave me with a almost new 64gb working iPhone and a 16gb "for parts" iPhone. Please help me out with this if you have any knowledge

~Aloha

Brandon