The evolution of halos with masses around Mh≈1011M⊙ and Mh≈1012M⊙ at redshifts z>9 is examined using constrained N-body simulations. {The average specific mass accretion rates, M˙h/Mh, exhibit minimal mass dependence and generally agree with existing literature. Individual halo accretion histories, however, vary substantially. } About one-third of simulations reveal an increase in M˙h around z≈13. Comparing simulated halos with observed galaxies having spectroscopic redshifts, we find that for galaxies at z≳9, the ratio between observed star formation rate (SFR) and M˙h is approximately 2%. This ratio remains consistent for the stellar-to-halo mass ratio (SHMR) but only for z≳10. At z≃9, the SHMR is notably lower by a factor of a few. At z≳10, there is an agreement between specific star formation rates (sSFRs) and M˙h/Mh. However, at z≃9, observed sSFRs exceed simulated values by a factor of two. It is argued that the mildly elevated SHMR in high-z halos with Mh≈1011M⊙, can be achieved by assuming the applicability of the local Kennicutt-Schmidt law and a reduced effectiveness of stellar feedback due to deeper gravitational potential of high-z halos of a fixed mass.