Muhly and Solel developed a notion of Morita equivalence for $C^*$-correspondences, and they proved a very important result: If two injective $C^*$-correspondences are Morita equivalent then the corresponding Cuntz-Pimsner algebras are strong Morita equivalent in the sense of Rieffel. Instead of proving this directly, we build a functor that will give us the result of Muhly and Solel, in fact a more generalized version of their result, as a special case.