Who came up with the concept of the unmoved mover?

It was Aristotle who came up with the concept of the unmoved mover. His focus was on 'that which moves without being moved' or prime mover (Latin: primum movens). It is a concept strongly advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. It was the theologian St. Thomas Aquinas who elaborated on the unmoved mover in the 'Quinque viae', five logical arguments regarding the existence of God summarized by Aquinas in his book "Summa Theologica".

For Aristotle, he must show that the universe is a single causal system. He works through an examination of the notion of movement, which finds its culmination in Book XI of his "Metaphysics". Motion, for Aristotle, refers to change in any of several different categories. Aristotle’s fundamental principle is that everything that is in motion is moved by something else, and he offers a number of arguments to this effect. He then argues that there cannot be an infinite series of moved movers. If it is true that when A is in motion there must be some B that moves A, then if B is itself in motion there must be some C moving B, and so on. This series cannot go on forever, and so it must come to a halt in some X that is a cause of motion but does not move itself—an unmoved mover.