  The Bekenstein's theorem allows us to generate a Einstein-conformal scalar
solution from a single Einstein-ordinary scalar solution. In this article, we
extend this theorem to Einstein-Maxwell-scalar (EMS) theory with a non-minimal
coupling between the scalar and Maxwell field. As applications of this extended
theorem, the well-known static dilaton solution and rotating solution with a
specific coupling between dilaton and Maxwell field are considered, and new
conformal dilaton black hole solutions are found. The Noether charges such as
the mass, electric charge, angular momentum are compared between the old and
new black hole solutions connected by conformal transformations, and they are
found conformally invariant. We speculate that the theorem may be helpful in
the computations of metric perturbations and spontaneous scalarization of black
holes in the Einstein-Maxwell-conformal-scalar theory since they can be mapped
to the corresponding EMS theories, which have been investigated in detail.
