  We study Lie algebroids in positive characteristic and moduli spaces of their
modules. In particular, we show a Langton's type theorem for the corresponding
moduli spaces. We relate Langton's construction to Simpson's construction of
gr-semistable Griffiths transverse filtration. We use it to prove a recent
conjecture of Lan-Sheng-Zuo that semistable systems of Hodge sheaves on
liftable varieties in positive characteristic are strongly semistable.
