The paper deals with the application of the method of eigenfunctions of the S-matrix to the problem of two zero range potentials and continues our study of photodetachment, begun in a previous paper (Devdariani, Dadonova 2018). In the case under consideration the eigenfunctions of specific parity depend on two phases that lead to the explicit expressions for the characteristics of scattering and make it possible to construct the proper sets of wave functions for the problems of scattering and photodetachment. An interesting feature of the problem is that the two phases can coincide, which leads to a resonance in the transmission coefficient.