  In this paper, we study extensions between two finite irreducible conformal
modules over the Schr\"odinger-Virasoro conformal algebra and the extended
Schr\"odinger-Virasoro conformal algebra. Also, we classify all finite
nontrivial irreducible conformal modules over the extended
Schr\"odinger-Virasoro conformal algebra. As a byproduct, we obtain a
classification of extensions of Heisenberg-Virasoro conformal modules.
