Spin-depending scattering is studied on a two-dimensional quantum network constructed of a quantum well with three semi-infinite quantum wires (an input wire and two terminals ) attached to it. The spin-orbital interaction causing selective scattering in the network is described by the Rashba Hamiltonian. The transmission of electrons across the well from the input quantum wire to terminals is caused by the excitation of a resonance oscillatory spin-mode in the well. For thin quantum networks we suggest also an approximate formula which defines the resonance transmission of electrons across the quantum well, depending on the shape of the standing spin-mode in the quantum well.