Using the non-equilibrium statistical operator method (NSO), we have investigated the spin transport through the interface in a semiconductor/ferromagnetic insulator hybrid structure. We have analyzed the approximation of effective parameters, when each of the considered subsystems (conduction electrons, magnons, and phonons) is characterized by its effective temperature. We have constructed the macroscopic equations, describing the spinwave current caused by both resonantly excited spin system of conduction electrons and by an inhomogeneous thermal field in the ferromagnetic insulator.