  We study congruences on the partial automorphism monoid of a finite rank free
group action. We give a decomposition of a congruence on this monoid into a
Rees congruence, a congruence on a Brandt semigroup and an idempotent
separating congruence. The constituent parts are further described in terms of
subgroups of direct and semidirect products of groups. We utilize this
description to demonstrate how the number of congruences on the partial
automorphism monoid depends on the group and on the rank of the action.
