Reading 'The Mind’s I'

In the book entitled The Mind’s I, by Douglas Hofstadter, philosopher Daniel C. Dennett posed the following problem: Suppose you are an astronaut stranded on Mars whose spaceship has broken down beyond repair. In your disabled craft there is a Teleclone Mark IV teleporter that can swiftly and painlessly dismantle your body, producing a molecule-by-molecule blueprint to be beamed to Earth.

There, a Teleclone receiver stocked with the requisite atoms will produce, from the beamed instructions, you—complete with all your memories, thoughts, feelings, and opinions. If you activate the Teleclone Mark IV, which astronaut are you—the one dismantled on Mars or the one produced from a blueprint on Earth? Suppose further that an improved Teleclone Mark V is developed that can obtain its blueprint without destroying the original. Are you then two astronauts at once? If not, which one are you?

After first reading this essay option, I thought the section concerning the Teleclone Mark Ⅳ was no more than a trick. If I was dismantled on Mars, presumably I would remember pressing the button, and the next thing I knew I'd be on earth. Then, of course, the duplicate on earth would be me since, within the complete genetic copy, all the same memories, physical and mental conditions would render me exactly the same for all practical purposes.

But what about the soul? To most non-religious people, the only evidence that might show the existence of a soul is the body’s immediate loss of 21 grams after death. However, this explanation endows the soul with a physical attribute, contradicting the theological definition of a soul. If we consider the effects of the Teleclone Mark IV on a human with such a theological spirit, we should expect that, while the machine produces a molecule-by-molecule blueprint to be beamed to Earth, the soul, which is not a physical object, would not be transmitted. If, according to Christianity, a soul is the symbol of unique individuality, then, upon pressing the button, such a person would be the duplicate on Earth in a physical sense, but would cease to be in a spiritual sense. Some reject the idea of a soul and may, in a larger sense, doubt the existence of God. It seems to me that, upon pressing the button, such a person would become the duplicate on Earth in the most complete sense.
The Teleclone Mark IV’s upgrade provides an even more complex scenario. There seem to be four logical options: A, I am on Mars; B, I am on Earth; C, I am on both Mars and Earth; D, I am on neither of the two planets.
As I understand it, this whole problem regarding which astronaut I am is posed in order to prompt me to explore what defines a unique being, that is, the identity of an individual.The notion of two identical beings raises a larger question: Am I identical to myself throughout space and time? Teleporting astronauts make us to consider our identities in different spaces, but what about in different times?