  We re-interpret Goodwin's translation functors for a finite $W$-algebra
$H_\ell$ as an action of a monoidal subcategory of $U(\mathfrak{g})$-mod on the
category of finitely generated $H_\ell$-modules. This action is obtained by
transporting the tensor product of $U(\mathfrak{g})$-modules through Skryabin's
equivalence. We apply this interpretation to show that the Skryabin equivalence
by stages introduced by Genra and Juillard is an equivalence of
$U(\mathfrak{g})$-module categories.
