  Subsequent to the Moon's formation, late accretion to the terrestrial planets
strongly modified the physical and chemical nature of silicate crusts and
mantles. This alteration came in the form of melting through impacts, as well
as the belated addition of volatiles and the highly siderophile elements
(HSEs). Current debate centres on whether the lunar HSE record is
representative of its whole late accretion history or alternatively that these
were only retained in the mantle and crust after a particular time, and if so,
when. Here we employ improved Monte Carlo impact simulations of late accretion
onto the Moon and Mars and present an updated chronology based on new dynamical
simulations of leftover planetesimals and the E-belt. We take into account the
inefficient retention of colliding material. We compute the crater and basin
densities on the Moon and Mars, the largest objects to strike these planets and
the amount of material they accreted. Outputs are used to infer the mass in
leftover planetesimals at a particular time period, which is then compared to
the lunar HSE abundance. From this estimate we calculate a preferred lunar HSE
retention age of ca. 4450 Ma which means that the modelled lunar mantle HSE
abundances trace almost all of lunar late accretion. Based on our results, the
surface ages of the lunar highlands are at least 4370 Ma. We find that the mass
of leftover planetesimals with diameters Di<300 km at 4500 Ma that best fits
the crater chronology is approximately 2x10^{-3} Earth mass (ME) while the mass
of the E-belt was fixed at 4.5x10^{-4} ME. We also find that a leftover
planetesimal mass in excess of 0.01 ME results in a lunar HSE retention age
younger than major episodes of lunar differentiation and crust formation, which
in turn violates geochemical constraints for the timing and intensity of late
accretion to the Earth (Mojzsis et al., 2019).
