  Starting from a real analytic surface $\mathcal{M}$ with a real analytic
conformal Cartan connection A. Bor\'owka constructed a minitwistor space of an
asymptotically hyperbolic Einstein-Weyl manifold with $\mathcal{M}$ being the
boundary. In this article, starting from a symmetry of conformal Cartan
connection, we prove that symmetries of conformal Cartan connection on
$\mathcal{M}$ can be extended to symmetries of the obtained Einstein-Weyl
manifold.
