  The first hydrostatic core (FHSC) phase is a brief stage in the protostellar
evolution that is difficult to detect. Our goal is to characterize the chemical
evolution of gas and dust during the formation of the FHSC. Moreover, we are
interested in analyzing, for the first time with 3D magnetohydrodynamic (MHD)
simulations, the role of grain growth in its chemistry. We postprocessed
$2\times10^{5}$ tracer particles from a $\texttt{RAMSES}$ non-ideal MHD
simulation using the codes $\texttt{NAUTILUS}$ and $\texttt{SHARK}$ to follow
the chemistry and grain growth throughout the simulation. A great chemical
inheritance is seen, as gas-phase abundances of most of the C, O, N, and S
reservoirs in the hot corino at the end of the simulation match the ice-phase
abundances from the prestellar phase. Additionally, interstellar complex
organic molecules (iCOMs) such as methyl formate, acetaldehyde, and formamide
are formed during the warm-up process. The typical grain size in the hot corino
$(n_{\rm H}>10^{11}\ {\rm cm^{-3}})$ increases forty-fold during the last 30
kyr, with negligible effects on its chemical composition. At moderate densities
$(10^{10}<n_{\rm H}<10^{11}\ {\rm cm^{-3}})$ and cool temperatures $15<T<50$ K,
increasing grain sizes delay molecular depletion. Finally, at low densities
$(n_{\rm H}\sim10^{7}\ {\rm cm^{-3}})$, grains do not grow significantly. We
also compared our results with a two-step model that reproduces well the
abundances of C and O reservoirs, but not the N and S reservoirs. We conclude
that the chemical composition of the FHSC is heavily determined by that of the
parent prestellar core, chemo-MHD computations are needed for an accurate
prediction of the abundances of the main N and S elemental reservoirs, and that
the impact of grain growth in moderately dense areas delaying depletion permits
the use of abundance ratios as grain growth proxies.
