  We show that indecomposable exact module categories over the category Rep H
of representations of a finite-dimensional Hopf algebra H are classified by
left comodule algebras, H-simple from the right and with trivial coinvariants,
up to equivariant Morita equivalence. Specifically, any indecomposable exact
module categories is equivalent to the category of finite-dimensional modules
over a left comodule algebra. This is an alternative approach to the results of
Etingof and Ostrik. For this, we study the stabilizer introduced by Yan and Zhu
and show that it coincides with the internal Hom. We also describe the
correspondence of module categories between Rep H and Rep (H^*).
