We develop a theoretical model to describe two-beam energy exchange in a hybrid photorefractive inorganic-cholesteric cell. A cholesteric layer is placed between two inorganic substrates. One of the substrates is photorefractive (Ce:SBN). Weak and strong light beams are incident on the hybrid cell. The interfering light beams induce a periodic space-charge field in the photorefractive window. This penetrates into the cholesteric liquid crystal (LC), inducing a diffraction grating written on the LC director. In the theory, the flexoelectric mechanism for electric field-director coupling is more important than the LC static dielectric anisotropy coupling. The LC optics is described in the Bragg regime. Each beam induces two circular polarized waves propagating in the cholesteric cell with different velocities. The model thus includes optical rotation in the cholesteric LC. The incident light beam wavelength can fall above, below, or inside the cholesteric gap. The theory calculates the energy gain of the weak beam, as a result of its interaction with the pump beam within the diffraction grating. Theoretical results for exponential gain coefficients are compared with experimental results for hybrid cells filled with cholesteric mixture BL038/CB15 at different concentrations of chiral agent CB15. Reconciliation between theory and experiment requires the inclusion of a phenomenological multiplier in the magnitude of the director grating. This multiplier is cubic in the space-charge field, and we provide a justification of the q-dependence of the multiplier. Within this paradigm, we are able to fit theory to experimental data for cholesteric mixtures with different spectral position of cholesteric gap relative to the wavelength of incident beams, subject to the use of some fitting parameters.