Automorphisms of Salem degree 22 on supersingular K3 surfaces of higher Artin invariant

We give a short proof that every supersingular K3 surface (except possibly in characteristic 2 with Artin invariant sigma = 10) has an automorphism of Salem degree 22. In particular an infinite subgroup of the automorphism group does not lift to characteristic zero. The proof relies on the case sigma = 1 and the cone conjecture for K3 surfaces.