According to quantum mechanics, there is indeed a non-zero probability of finding an electron anywhere in space, including the region around the Moon. However, it is important to note that the probability decreases significantly as you move away from the vicinity of the electron's associated atom.
Atoms are composed of a nucleus (containing protons and neutrons) surrounded by a cloud of electrons. The electrons occupy specific energy levels or orbitals around the nucleus. These orbitals have different shapes and sizes, and they determine the probability distribution of finding an electron in a particular region of space.
While there is a non-zero probability of finding an electron from an atom of your body on the Moon, the probability is extremely low due to the vast distances involved and the shielding effects of other atoms in your body. The likelihood of an entire atom from your body being located on the Moon is practically negligible.
In terms of falsifiability, it would be challenging to directly test or prove the presence of a specific atom from your body on the Moon. The detection and identification of individual atoms on the Moon would require highly advanced and sensitive techniques. Furthermore, the number of atoms in your body is enormous, and it would be extremely difficult to trace the origin of a specific atom back to your body.
Therefore, while the claim of finding an atom from your body on the Moon is theoretically possible due to the probabilistic nature of quantum mechanics, practically speaking, it is highly improbable and difficult to verify.