We propose a novel mechanism for the transfer of excitons as an entity through barriers in quantum well structures, namely by the emission of a single longitudinal optical (LO) phonon. The process arises from a combination of the Fröhlich coupling of electrons and holes to the LO phonons and the admixture of different subband states to the wave function of the excitons due to the Coulomb interaction. For the case of an asymmetric double quantum well, a numerical calculation of the resulting relaxation rates is given. We show that the process can dominate over the separate transfer of electrons and holes.