  The elusive properties of the first (Pop III) stars can be indirectly
unveiled by uncovering their true descendants. To this aim, we exploit our
data-calibrated model for the best-studied ultra-faint dwarf (UFD) galaxy,
Bo\"otes I, which tracks the chemical evolution (from carbon to zinc) of
individual stars from their formation to the present day. We explore the
chemical imprint of Pop III supernovae (SNe), with different explosion energies
and masses, showing that they leave distinct chemical signatures in their
descendants. We find that UFDs are strongly affected by SNe-driven feedback
resulting in a very low fraction of metals retained by their gravitational
potential well (< 2.5 %). Furthermore, the higher the Pop III SN explosion
energy, the lower the fraction of metals retained. Thus, the probability to
find descendants of energetic Pair Instability SNe is extremely low in these
systems. Conversely, UFDs are ideal cosmic laboratories to identify the
fingerprints of less massive and energetic Pop III SNe through their [X/Fe]
abundance ratios. Digging into the literature data of Bo\"otes I, we uncover
three hidden Pop III descendants: one mono-enriched and two multi-enriched.
These stars show the chemical signature of Pop III SNe in the mass range
$[20-60]\rm M_{\odot}$, spanning a wide range in explosion energies $[0.3-5]
10^{51}$ erg. In conclusion, Pop III descendants are hidden in ancient UFDs but
those mono-enriched by a single Pop III SN are extremely rare. Thus,
self-consistent models such as the one presented here are required to uncover
these precious fossils and probe the properties of the first Pop III
supernovae.
