Ok, that makes much more sense. The change in the magnetic flux induces an electrical field, so the wire does not need to pay any attention to anything but to the existence (or not) of an electric field. This way the "memory problem" is solved: once there is an electric field (and the wire does...
If we have a metal wire and a magnetic field "inside" it, when the flux of the magnetic field changes, then the wire "reacts" by "creating" an induced current.
After learning this law, it eventually came to my mind the question: how does the wire know that the magnetic field flux has changed...