There is no connection. None. Not Nefesh, not Ruach, not Neshama, not Chaya, not Yechida —none of these are within us. There is nothing in this body that belongs to the soul. There is a vital force, like in animals, but nothing more.

Why should your body, which is entirely animalistic, at the level of the "living," entirely replaceable by various parts. 

We do not call this body "human" (Adam). We call it that arbitrarily, but it is not human. A human (Adam) is resembling the Creator, resembling the force of giving and love, and that is why it is called Adam, meaning "similar to the Upper" (Domeh le Elyon). So, an attribute, a quality of giving and love, that resembles the Creator is called Adam. Adam, from the word Domeh (meaning "similar". in hebrew) Therefore, calling something Adam or soul can mean the same thing.

Here we come to two very unique points. Resembling the Creator means that, out of my qualities, I shape myself to resemble the Creator. To the extent that I resemble Him, I am called Adam. I prepare within myself qualities that allow a part of the Creator, called the soul, to clothe within me. What I prepare for receiving this soul is also called the "body of the soul," and what enters into this body of the soul is called its inner essence, or the soul itself, or light (Or).

Yes, I must create the body of the soul. To the extent that this body resembles the Creator, it is called Adam, from the word Domeh (similar to the Creator). Then the soul enters this body. This body is made up of the qualities of giving and love that I myself have shaped. It is in this body, not the physical body, that the soul resides.