  A surjective Morita context connecting semigroups $S$ and $T$ yields a Morita
semigroup and a strict local isomorphism from it onto $S$ along which
idempotents lift. We describe strong Morita equivalence of firm semigroups in
terms of Morita semigroups and isomorphisms. We also generalize some of
Hotzel's theorems to semigroups with weak local units. In particular, the
Morita semigroup induced by a dual pair $\beta$ over a semigroup with weak
local units is isomorphic to $\Sigma ^\beta$.
