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The Green's functions for the magnetic scalar and electric vector potentials are derived for a rectangular waveguide with dielectric-filled corrugations supporting left-hand, as well as right-hand propagation. The derivation of the Green's functions for this pair of auxiliary potentials is more involved than their electric-type counterparts. An investigation of the divergence of the electric vector potential is performed with emphasis on the waveguide transverse electric modes. As a result of the divergenceless nature of the vector potential for these modes, the scalar potential is shown to vanish within the corrugations, and the rest of the derivation proceeds by employing the spectral representation then transforming back to the spatial domain. The derived expressions are verified by considering some examples involving discontinuities that can be modeled by equivalent magnetic currents in view of the equivalence principle. Comparison with full-wave simulation commercial packages validates the current theory.