  The shape of the low-mass (faint) end of the galaxy stellar mass function
(SMF) or ultraviolet luminosity function (UVLF) at z > 6 is an open question
for understanding which galaxies primarily drove cosmic reionisation. Resolved
photometry of Local Group low-mass galaxies allows us to reconstruct their star
formation histories, stellar masses, and UV luminosities at early times, and
this fossil record provides a powerful `near-far' technique for studying the
reionisation-era SMF/UVLF, probing orders of magnitude lower in mass than
direct HST/JWST observations. Using 882 low-mass (Mstar < 10^9 Msun) galaxies
across 11 Milky Way- and Local Group-analogue environments from the FIRE-2
cosmological baryonic zoom-in simulations, we characterise their progenitors at
z ~ 6 - 9, the mergers/disruption of those progenitors over time, and how well
their present-day fossil record traces the high-redshift SMF. A present-day
galaxy with Mstar ~ 10^5 Msun (10^9 Msun) had ~1 (~30) progenitors at z ~ 7,
and its main progenitor comprised ~100% (~50%) of the total stellar mass of all
its progenitors at z ~ 7. We show that although only ~ 15% of the early
population of low-mass galaxies survives to present day, the fossil record of
surviving Local Group galaxies accurately traces the low-mass slope of the SMF
at z ~ 6 - 9. We find no obvious mass dependence to the mergers and accretion,
and show that applying this reconstruction technique to just the low-mass
galaxies at z = 0 and not the MW/M31 hosts correctly recovers the slope of the
SMF down to Mstar ~ 10^4.5 Msun at z > 6. Thus, we validate the `near-far'
approach as an unbiased tool for probing low-mass reionisation-era galaxies.
