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With semi-quantum theory, we quantitatively deduce microwave photons radiated from the moving electrons in a magnetic field, as well as the interaction of transmitted microwave photons with the vortex electrons in the magnetic field. It shows that the Orbital Angular Momentum (OAM) transition between microwave photons and vortex electrons in the magnetic field occurs when the relativistic effect is considered. This work indicates an effective way to transfer OAM between microwave photons and vortex electrons theoretically. By the OAM microwave photon resonance absorption, different vortex electrons with radial and magnetic quantum numbers can be generated. Furthermore, vortex electrons can be detected to analyze the OAM carried by microwave photons.