in figure 7, Faradays Law: changing magnetic field in the left torus induces a variable current in the wire, then via ampere's law the changing current in the wire induces a magnetic field in the second torus.

However in figure 8 while there is an A field which extends to infinity, don't forget that B = curl(A) and so the magnetic field of the torus is going to be confined within it. As such there's no way to induce a new field in the additional torus. A is a potential, it's not a "real" field in as much as you can only measure things like |B| and |E| (or quantum phases induced by A in the Ahranovov-Bohm experiment)

You need a current to flow in order to induce a magnetic field in the second iron ring.