  Despite extensive search efforts, direct observations of the first (Pop III)
stars have not yet succeeded. Theoretical studies have suggested that late Pop
III star formation is still possible in pristine clouds of high-mass galaxies,
coexisting with Pop II stars, down to the Epoch of Reionization (EoR). Here we
reassess this finding by exploring Pop III star formation in six $50h^{-1}
~$cMpc simulations performed with the hydrodynamical code dustyGadget. We find
that Pop III star formation ($\sim 10^{-3.4} - 10^{-3.2} ~ \mathrm{M_\odot
yr^{-1} cMpc^{-3}}$) is still occurring down to $z \sim 6 - 8$, i.e. well
within the reach of deep JWST surveys. At these epochs, $\gtrsim 10 \%$ of the
rare massive galaxies with $M_\star \gtrsim 3 \times 10^9 ~ \mathrm{M_\odot}$
are found to host Pop III stars, although with a Pop III/Pop II mass fraction
$\lesssim 0.1 \%$. Regardless of their mass, Pop III hosting galaxies are
mainly found on the main sequence, at high star formation rates, probably
induced by accretion of pristine gas. This scenario is also supported by their
increasing star formation histories and their preferential location in
high-density regions of the cosmic web. Pop III stars are found both in the
outskirts of metal-enriched regions and in isolated, pristine clouds. In the
latter case, their signal may be less contaminated by Pop IIs, although its
detectability will strongly depend on the specific line-of-sight to the source,
due to the complex morphology of the host galaxy and its highly inhomogeneous
dust distribution.
