The geometry-dependent energy transfer rate from an electrically pumped inorganic semiconductor quantum well into an organic molecular layer is studied theoretically. We focus on Förster-type nonradiative excitation transfer between the organic and inorganic layers and include quasimomentum conservation and intermolecular coupling between the molecules in the organic film. (Transition) partial charges calculated from density-functional theory are used to calculate the coupling elements. The partial charges describe the spatial charge distribution and go beyond the common dipole-dipole interaction. We find that the transfer rates are highly sensitive to variations in the geometry of the hybrid inorganic-organic system. For instance, the transfer efficiency is improved by up to 2 orders of magnitude by tuning the spatial arrangement of the molecules on the surface: Parameters of importance are the molecular packing density along the effective molecular dipole axis and the distance between the molecules and the surface. We also observe that the device performance strongly depends on the orientation of the molecular dipole moments relative to the substrate dipole moments determined by the inorganic crystal structure. Moreover, the operating regime is identified where inscattering dominates over unwanted backscattering from the molecular layer into the substrate.