  We prove a rigidity theorem for semi-arithmetic Fuchsian groups: If
$\Gamma_1$, $\Gamma_2$ are two semi-arithmetic lattices in
$\mathrm{PSL}(2,\mathbb{R})$ virtually admitting modular embeddings and
$f\colon\Gamma_1\to\Gamma_2$ is a group isomorphism that respects the notion of
congruence subgroups, then $f$ is induced by an inner automorphism of
$\mathrm{PGL}(2,\mathbb{R})$.
