  We construct a functor that maps $C^*$-correspondences to their Cuntz-Pimsner
algebras. Applications include a generalization of the well-known result of
Muhly and Solel: Morita equivalent $C^*$-correspondences have Morita equivalent
Cuntz-Pimsner algebras; as well as the result of Muhly, Pask, and Tomforde:
regular strong shift equivalent $C^*$-correspondences have Morita equivalent
Cuntz-Pimsner algebras.
