We derive the equations for eigenstates and eigenenergies of a triple
magnetopolaron in quantum-well structures. An iteration procedure for
obtaining the wave function and energy including the contributions of
diagrams with crossing phonon lines is given. We show that under condi
tions of exact resonance the middle energy branch of the triply split
magnetopolaron state consists of only two out of three bare states. We
suggest the experimental verification of this prediction.