Electron beam longitudinal polarization during the interaction with counterpropagating circularly-polarized ultraintense laser pulses is investigated, while accounting for the anomalous magnetic moment of the electron. Although it is known that the helicity transfer from the laser photons to the electron beam is suppressed in linear and nonlinear Compton scattering processes, we show that the helicity transfer nevertheless can happen via an intermediate step of the electron radiative transverse polarization, phase-matched with the driving field, followed up by spin rotation into the longitudinal direction as induced by the anomalous magnetic moment of the electron. With spin-resolved QED Monte Carlo simulations, we demonstrate the consequent helicity transfer from laser photons to the electron beam with a degree up to 10%, along with an electron radial polarization up to 65% after multiple photon emissions in a femtosecond timescale. This effect is detectable with currently achievable laser facilities, evidencing the role of the leading QED vertex correction to the electron anomalous magnetic moment in the polarization dynamics in ultrastrong laser fields.
