A counter-intuitive disappearance of the giant terahertz photoconductance of a quantum point contact (QPC) under increase in the photon energy, which was discovered experimentally (Otteneder et al., Phys. Rev. Applied 10 (2018) 014015) and studied by the numerical calculations of the photon-stimulated transport (O.A. Tkachenko et al., JETP Lett. 108 (2018) 396), is explained here by using qualitative considerations about the momentum conservation upon absorption of terahertz photons. The spectra of photon-stimulated transmission through a smooth one-dimensional barrier are calculated on the basis of the perturbation theory. These calculations also predict the spectral maxima for optical transitions from the Fermi level to the top of the potential barrier. Within the proposed physical picture, the widths of the spectral maxima are estimated, and the evolution of the shape of the spectra with a change in the position of the Fermi level is qualitatively explained.