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One or several resonant hole states related to the absolute reflection at hole scattering on a quantum well were found to exist in the energy range where only heavy holes may propagate over barriers in a quantum-well heterostructure. Energies of resonant states are close to those of peaks of absolute reflection. The qualitative behaviour of the over-barrier scattering and resonant states is the same at variation of quantum well shape and depth, however lifetimes of resonant states depend strongly on all parameters. These long-lived resonant states may be one of the reasons for the efficient hole capture by quantum wells.