  The Blok-Esakia theorem states that there is an isomorphism from the lattice
of intermediate logics onto the lattice of normal extensions of Grzegorczyk
modal logic. The extension for multi-conclusion consequence relations was
obtained by Emil Je\v{r}\'abek as an application of canonical rules. We show
that Je\v{r}\'abek's result follows already from Blok's algebraic proof.
  We also prove that the properties of strong structural completeness and
strong universal completeness are preserved and reflects by the aforementioned
isomorphism. These properties coincide with structural completeness and
universal completeness respectively for single-conclusion consequence relations
and, in particular, for logics.
