  We establish the Schauder estimates at the boundary away from the
characteristic points for the Dirichlet problem by means of the double layer
potential in a Heisenberg-type group $\mathbb{G}$. Despite its singularity we
manage to invert the double layer potential restricted to the boundary thanks
to a reflection technique for an approximate operator in $\mathbb{G}$. This is
the first instance where a reflection-type argument appears to be useful in the
sub-Riemannian setting.
