Self Homotopy equivalences of Postnikov conjugates

The purpose of this note is to generalize a result of Wilkerson [4] and show that the self homotopy equivalences of the Postnikov approximations of a space X determine, in a rather simple manner, simultaneously the self homotopy equivalences of X and the self homotopy equivalences of the Postnikov conjugates of X (i.e. the spaces with the same Postnikov approximations as X).