  We show that for any integer n and any field k of characteristic different
from 2 there are at most finitely many isomorphism classes of quadratic
morphisms from the projective line over k to itself with a finite postcritical
orbit of size n. As a consequence we prove that every postcritically finite
quadratic morphism over a field of positive characteristic can be lifted to
characteristic zero with the same combinatorial type of postcritical orbit. The
associated profinite geometric monodromy group is therefore the same as in
characteristic zero, where it can be described explicitly by generators as a
self-similar group acting on a regular rooted binary tree.
