We develop a theoretical model to describe two-beam energy exchange in a hybrid photorefractive inorganic-cholesteric cell. A cholesteric LC cell is placed between two inorganic photorefractive windows. Weak and strong light beams are incident on the LC cell. The interfering light beams induce a periodic space-charge field in the photorefractive windows. This penetrates into the LC, inducing a diffraction grating written on the LC director. The theory calculates the energy gain of the weak beam, as a result of its interaction with the pump beam within the diffraction grating. In the theory, the flexoelectric mechanism for electric field-director coupling is a more important than the LC static dielectric anisotropy coupling. The flexoelectric polarization in the bulk LC follows from the initial director pretilt at the cell substrates and is the main physical mechanism governing the magnitude of the director grating and the two-beam coupling. The LC optics is described in the Bragg regime. Theoretical results for exponential gain coefficients have been compared with experimental results for hybrid cells filled with cholesteric mixtures TL205/CB15 and BL038/CB15. In order to reconcile theory and experiment, we require that (a) the magnitude of the director grating must be cubic rather than linear in the space-charge field, and (b) near the cell surface, nematic ordering must dominate. Within this paradigm, we are able to fit experimental data to theory for both cholesteric mixtures, subject to the use of some fitting parameters.