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The Sun albedo of cosmic rays at GeVs energy has been discovered recently byFERMI satellite. They are traces of atmospheric CR hitting solar atmosphere andreflecting skimming gamma photons. Even if relevant for astrophysics, as beingtrace of atmospheric solar Cosmic Ray noises they cannot offer any signal ofneutrino astronomy. On the contrary the Moon, with no atmosphere, may becomesoon a novel filtering calorimeter and an amplifier of energetic muonastronomical neutrinos (at TeV up to hundred TeV energy); these lepton tracksleave an imprint in their beta decay while in flight to Earth. Their TeVelectron air-shower are among the main signals. Also a more energetic, but morerare, PeV up to EeV tau lunar neutrino events may be escaping as a tau leptonfrom the Moon: PeVs secondaries may be shining on Earth atmosphere in lunarshadows in a surprising rich way. One or a few gamma air-shower event insidethe Moon shadows may occur each year in near future CTA or LHAASO TeVs gammaarray detector, assuming a non negligible astrophysical TeV up to hundred TeVneutrino component (respect to our terrestrial ruling atmospheric ones); thesesignals will open a new wonderful passepartout keyhole for neutrino been seenalong the Moon. The lunar solid angle is small and the muon or tau expectedrate is rare, but future largest tau radio array as GRAND one might welldiscover such neutrino imprint.

Signals of HE atmospheric muon decay in flight around the Sun's albedo versus astrophysical muon and tau neutrino traces in the Moon's shadow