with ${\stackrel{\textup{SME}}{\thicksim}}$ by a $\si$-TRO. Notice that we do not make a distinction between unitary equivalence and isomorphism in the category of operator bimodules. In particular we show that they coincide for C\*-correspondences by viewing the linking algebra as the C\*-envelope of an appropriate subalgebra (Proposition \[P: uneq=cc\]). Our methods then use a fundamental result of Blecher [@Ble97] which states that the stabilized tensor product coincides with the balanced Haagerup tensor product for non-degenerate C\*-correspondences.

Although we include it in all statements, it is worth mentioning here that C\*-correspondences (and thus all representations) are considered to be non-degenerate. This is not an artifact for convenience. Strong Morita equivalence automatically induces non-degeneracy of the C\*-correspondences.

Preliminaries
=============

The reader should be well acquainted with the theory of operator algebras [@BleLeM04; @Pau02]. For an exposition on the C\*-envelope s/he may refer to [@KakNotes]. Furthermore the reader should be familiar with the general theory of Hilbert modules and C\*-correspondences. For example see [@Lan95; @ManTro01] for Hilbert modules and [@Kat04; @MuhSol98] for C\*-correspondences. We will give a brief introduction for purposes of notation and terminology.

C\*-correspondences
-------------------

A C\*-correspondence ${}_A X_B$ is a right Hilbert module $X$ over $B$ along with a $*$-homomorphism $\phi_X 