Let be a countable ergodic group G of automorphisms of a measure space and N be the normalizer of its full group . Problem: for a pair of measurable partitions of the space, when does there exist an element in N that comjugates these partitions. For a wide class of measurable partitions, we give a solution to this problem in the case where G is an approximately finite group with finite invariant measure. As a consequence, we obtain results concerning the conjugacy of the commutative subalgebras that correspond to the given partitions in the type II_1 factor constructed via the orbit partition of the group .