  Strong increase in the intensity of the peaks of excited magneto-exciton (ME)
states in the photoluminescence excitation (PLE) spectra recorded for the
ground heavy-hole magneto-excitons (of the 1sHH type) has been found in a
GaAs/AlGaAs superlattice in strong magnetic field B applied normal to the
sample layers. While varying B the intensities of the PLE peaks have been
measured as functions of energy separation $\Delta E$ between excited ME peaks
and the ground state of the system. The resonance profiles have been found to
have maxima at $\Delta E_{\rm max}$ close to the energy of the GaAs LO-phonon.
However, the value of $\Delta E_{\rm max}$ depends on quantum numbers of the
excited ME state. The revealed very low quantum efficiency of the investigated
sample allows us to ascribe the observed resonance to the enhancement of the
non-radiative magneto-exciton relaxation rate arising due to LO-phonon
emission. The presented theoretical model, being in a good agreement with
experimental observations, provides a method to extract 1sHH magneto-exciton
``in-plane" dispersion from the dependence of $\Delta E_{\rm max}$ on the
excited ME state quantum numbers.
