  We consider the sedimentation of $N$ spherical particles with identical radii
$R$ in a Stokes flow in $\mathbb R^3$. The particles satisfy a no-slip boundary
condition and are subject to constant gravity. The dynamics of the particles is
modeled by Newton's law but with very small particle inertia as $N$ tends to
infinity and $R$ to $0$. In a mean-field scaling we show that the evolution of
the $N$-particle system is well approximated by the Vlasov-Stokes equation. In
contrast to the transport-Stokes equation considered in the first part of this
series, \cite{HoferSchubert23}, the Vlasov-Stokes equation takes into account
the (small) inertia. Therefore we obtain improved error estimates. We also
improve previous results on the Cauchy problem for the Vlasov-Stokes equation
and on its convergence to the transport-Stokes equation in the limit of
vanishing inertia. The proofs are based on relative energy estimates. In
particular, we show new stability estimates for the Vlasov-Stokes equation in
the $2$-Wasserstein distance. By combining a Lagrangian approach with a study
of the energy dissipation, we obtain uniform stability estimates for arbitrary
small particle inertia. We show that a corresponding stability estimate
continues to hold for the empirical particle density which formally solves the
Vlasov-Stokes equation up to an error. To this end we exploit certain uniform
control on the particle configuration thanks to results in the first part
\cite{HoferSchubert23}.
