According to the conservation of angular momentum, when a plane-wave polarized photon splits into a pair of electron-positron under the influence of the Coulomb field, the spin angular momentum (SAM) of the photon is converted into the angular momentum of the leptons. We investigate this process (the Bethe-Heitler process) by describing the final electron and positron with twisted states and find that the SAM of the incident photon is not only converted into SAM of the produced pair, but also into their orbital angular momentum (OAM), which has not been considered previously. The average OAM gained by the leptons surpasses the average SAM, while their orientations coincide. Both properties depend on the energy and open angle of the emitted leptons. The demonstrated spin-orbit transfer shown in the Bethe-Heitler process may exist in a large group of QED scattering processes.
