The phantom limb phenomenon is extremely surprising at first, however taking into account what we've learned about central pattern generators and corollary discharge it makes sense. Though the limb has been lost its connections to the rest of the nervous system still remain. Those connections are kind of like loose wires in a machine that keeps sending electricity towards another part of the machine without realizing that the other part is not receiving the electricity. Instead the electricity is being given off as sparks. The machine may keep sending electricity out until it breaks down or somebody turns it off.
The person can feel their missing limb because their nervous system tells them where the limb would be doing and what it would be doing, through the corollary discharge that the remaining central pattern generators (the remaining connections)send to surrounding neurons. This means that our perception of where our limbs are and what they are doing is a combination of sensory input we receive from the limb and other sources of sensory input as well as the information our nervous system receives from corollary discharge. Corollary discharge also represents what our nervous system wants our limbs to do, it is the message it is sending to the motor neurons. What happens however when the motor neurons can't do exactly what the nervous system tells them to do? What if they don't receive the message or if the muscles are not working properly? Who does the nervous system "believe", the corollary discharge that says that the limb has moved or the propioceptors that say the limb has not moved?
If the nervous system believes the propioceptors and the sensory input from the eyes, then the person should be able to convince themselves that the limb hasn't moved for some reason. If this is true then a person who faces the phantom limb syndrome should be able to convince themselves that their limb does not exist therefore they shouldn't be experiencing any sensation from it.
If the nervous system believes the corollary discharge signals then the person would have a very warped sense of reality and what is actually happening with their bodies in the world around them. This must be the dillema the person with phantom limbs must experience. They must be somewhere in between these two extremes.
Nice phrasing of the problem. Be a little careful, though, about details. The motoneurons are still around (though not connected to the muscles, which are missing). The CD signals almost certainly don't come from the motoneurons, but rather from CPG's which still also activate the motoneurons (actually, the motoneurons may, in time, disappear, and other secondary reorganizations may also take place in the nervous system). PG