The Sun albedo of Cosmic Rays (CRs) at GeVs energy has been discovered recently by the FERMI satellite. They are traces of atmospheric CRs hitting solar atmosphere and reflecting skimming gamma photons. Even if relevant for astrophysics, as being a trace of atmospheric solar CR noises they cannot offer any signal of neutrino astronomy. On the contrary, the Moon with no atmosphere, may become soon a novel filtering calorimeter and an amplifier of energetic muon astronomical neutrinos (at TeV up to hundred TeVs energy); these lepton tracks leave an imprint in their beta decay while in flight to Earth. Their TeV electron air-shower are among the main signals. Also, a more energetic, but more rare, PeV up to EeV tau lunar neutrino events may be escaping as a tau lepton from the Moon: (Formula presented.) PeV secondaries, then, may be shining on Earth’s atmosphere in lunar shadows in a surprising way. One or a few gamma air-shower events inside the Moon shadows may occur each year in near future Cherenkov telescope array (CTA) or large high altitude air shower observatory (LHAASO) TeV gamma array detector, assuming a nonnegligible astrophysical TeV up to hundred TeV neutrino component (with respect to our terrestrial ruling atmospheric ones); these signals will open a new wonderful passe-partout keyhole for neutrino, been seen along the Moon. The lunar solid angle is small and the muon or tau expected rate is rare, but with the future largest tau radio array as the giant radio array for neutrino detection (GRAND), one might well discover such neutrino imprint.