The binding energy of a polaron confined in the quantum well of GaAs/Ga 1− x Al x As double heterostructures is calculated as a function of the magnetic field applied in the direction of growth. We have also calculated the oscillator strength of electron-phonon interaction for transitions from various excited states to the ground state of the polaron. Every type of optical-phonon mode that can exist in such structures within the continuum model is considered separately. It is found that the magnetic field greatly enhances the interface-phonon part of the polaron effect. For quantum wells of widths 150 Å or smaller, the interface modes dominate all polaronic phenomena we have encountered when B≳ 1 T. For quantum wells of widths up to 100 Å, contributions from confined bulk phonon modes are almost negligible in magnetic fields B≳ 1 T.