  We revisit a central result of Muhly and Solel on operator algebras of
C*-correspondences. We prove that (possibly non-injective) strongly Morita
equivalent C*-correspondences have strongly Morita equivalent relative
Cuntz-Pimsner C*-algebras. The same holds for strong Morita equivalence (in the
sense of Blecher, Muhly and Paulsen) and strong $\Delta$-equivalence (in the
sense of Eleftherakis) for the related tensor algebras. In particular, we
obtain stable isomorphism of the operator algebras when the equivalence is
given by a $\sigma$-TRO. As an application we show that strong Morita
equivalence coincides with strong $\Delta$-equivalence for tensor algebras of
aperiodic C*-correspondences.
