The brain is the part of the body which is currently scientifically believed to be where consciousness is stored. Let us go on that assumption for now, simply because it is the easiest assumption to start from. There are other theories which suggest that consciousness is more connected with the world around us, or perhaps to other organs, but I have a feeling those are not the cases you are considering.
Now, consider the physical reality of a brain transplant. It is reasonable to treat the individual spinal neurons as communication channels. Each one goes "somewhere." As an infant, a great deal of our "mental activity" is pruning connections as we learn where each neuron goes. However, bodies are not the same. We cannot simply make a mapping of where every neuron went in one body, and look up the corresponding neuron. Some people simply have more sensory neurons than others, for instance. Biology is a messy process.
We would need some way to "roll back the clock" on the brain, and convince itself to return to a state experienced as an infant, telling it "all of your existing connections are wrong. Go reach out and find out what these ones do." One would literally have to learn every single motor skill over again.
Some connections would have to be done "right." For example, the nerve that innervates the diaphragm must be under brain control very early on (as in "by the first breath.") It's actually a rather large nerve (physically), so the doctors may have to identify it and attach it. Note that this points at a physiological reason for why a baby's first cry is such a big deal.
Some nerves would have to be attenuated until better signal identification can be made. For example, the cardiac nerves which control heart rate should probably be controlled loosely until the brain actually learns how to do it right.
One approach may be a very invasive version of physical therapy. Have a computer, assisted by a human, which can control the "essential" nerves like the breathing and heartrate ones, and dulls the others. Then, together, they can train the human brain to do the new activity.
However, there's a catch. We mentioned consciousness was in the brain. It is not yet known whether the circuitry that connects the brain to the body are a substantial part of the consciousness or not. We may find that the individual is a very different person in their new body. There are anecdotal claims of this with heart transplants, where a receiver of the transplant suddenly craves foods the donor used to eat. It is unclear the source of these anecdotes, but it is reasonable to presume that they will be more extreme with a full body transplant.