Electron interactions with interface phonon modes and strictly-confined bulk phonon modes are considered for the first time to calculate the magnetopolaronic effect on the transition energy of a hydrogenic impurity in the quantum well of a double heterostructure. The electron-phonon interaction is treated as a perturbation on a hydrogenic impurity confined in a quantum well under strongmagnetic fields. The unperturbed states are obtained by the variational method with trial wave functions constructed on symmetry considerations. It is found that the transition energy, as a function of the applied magnetic field, breaks up into three branches with two interaction gaps occuring at two-level and three-level resonances. The lowest branch lies below the bulk TO energy. These results are found in good agreement with recent experimental data.