  In this work we extend the non-ideal magnetohydrodynamics (MHD) solver in the
moving mesh code AREPO to include the Hall effect. The core of our algorithm is
based on an estimation of the magnetic field gradients by a least-square
reconstruction on the unstructured mesh, which we also used in the companion
paper for Ohmic and ambipolar diffusion. In an extensive study of simulations
of a magnetic shock, we show that without additional magnetic diffusion our
algorithm for the Hall effect becomes unstable at high resolution. We can
however stabilise it by artificially increasing the Ohmic resistivity,
$\eta_{\rm OR}$, so that it satisfies the condition $\eta_{\rm OR} \geq
\eta_{\rm H} /5$, where $\eta_{\rm H}$ is the Hall diffusion coefficient.
Adopting this solution we find second order convergence for the C-shock and are
also able to accurately reproduce the dispersion relation of the whistler
waves. As a first application of the new scheme, we simulate the collapse of a
magnetised cloud with constant Hall parameter $\eta_{\rm H}$ and show that,
depending on the sign of $\eta_{\rm H}$, the magnetic braking can either be
weakened or strengthened by the Hall effect. The quasi-Lagrangian nature of the
moving mesh method used here automatically increases the resolution in the
forming core, making it well suited for more realistic studies with
non-constant magnetic diffusivities in the future.
