  We show that if $M$ and $N$ are $C^{*}$-algebras and if $E$ (resp. $F$) is a
$C^{*}$-correspondence over $M$ (resp. $N$), then a Morita equivalence between
$(E,M)$ and $(F,N)$ implements a isometric functor between the categories of
Hilbert modules over the tensor algebras of $\mathcal{T}_{+}(E)$ and
$\mathcal{T}_{+}(F)$. We show that this functor maps absolutely continuous
Hilbert modules to absolutely continuous Hilbert modules and provides a new
interpretation of Popescu's reconstruction operator.
