Hybrid reflective intelligent surfaces (HRISs) can support localization in sixth-generation (6G) networks thanks to their ability to generate narrow beams and at the same time receive and process locally the impinging signals. In this paper, we propose a novel protocol for user localization in a network with an HRIS. The protocol includes two steps. In the first step, the HRIS operates in full absorption mode and the user equipment (UE) transmits a signal that is locally processed at the HRIS to estimate the angle of arrival (AoA). In the second step, the base station transmits a downlink reference signal to the UE, and the HRIS superimposes a message by a backscatter modulation. The message contains information on the previously estimated AoA. Lastly, the UE, knowing the position of the HRIS, estimates the time of flight (ToF) from the signal of the second step and demodulates the information on the AoA to obtain an estimate of its location. Numerical results confirm the effectiveness of the proposed solution, also in comparison with the Cram\'er Rao lower bound on the estimated quantities.nd on the estimated quantities.