  We show a few basic results about moduli spaces of semistable modules over
Lie algebroids. The first result shows that such moduli spaces exist for
relative projective morphisms of noetherian schemes, removing some earlier
constraints. The second result proves general separatedness Langton type
theorem for such moduli spaces. More precisely, we prove S-completness of some
moduli stacks of semistable modules. In some special cases this result
identifies closed points of the moduli space of Gieseker semistable sheaves on
a projective scheme and of the Donaldson--Uhlenbeck compactification of the
moduli space of slope stable locally free sheaves on a smooth projective
surface. The last result generalizes properness of Hitchin's morphism and it
shows properness of so called Hodge-Hitchin morphism defined in positive
characteristic on the moduli space of Gieseker semistable integrable
t-connections in terms of the p-curvature morphism. This last result was proven
in the curve case by de Cataldo and Zhang using completely different methods.
