In his original work, Josephson predicted that a phase-dependent conductance should be present in superconducting tunnel junctions, an effect difficult to detect, mainly because it is hard to single it out from the usual nondissipative Josephson current. We propose a solution for this problem that consists of using different superconducting materials to realize the two junctions of a superconducting interferometer. According to the Ambegaokar-Baratoff relation the two junctions have different conductances if the critical currents are equal, thus the Josephson current can be suppressed by fixing the magnetic flux in the loop at half of a flux quantum without canceling the phase-dependent conductance. Our proposal can be used to study the phase-dependent conductance, an effect present in principle in all superconducting weak links. From the standpoint of nonlinear circuit theory, such a device is in fact an ideal memristor with possible applications to memories and neuromorphic computing in the framework of ultrafast and low-energy-consumption superconducting digital circuits.