Let's say there's a closed conducting surface. Then by Gauss's Law the E field bound by the surface must equal the charge inside. There's no charge inside, so the E field cancels. This is a Faraday cage. There's no charge or electric field inside and and the charges on the exterior distribute themselves so as to cancel the E field.

My questions is this: let's say this first surface, is now enclosed completely within a second bigger surface, with the same properties, and they don't touch anywhere. Then the same thing would happen to the second Faraday cage, and so the E field inside would cancel. But if the E field inside cancels, then the charges on the first, now interior, Faraday cage redistribute themselves to their original positions, since they no longer need to compensate for any E field.

Is this right? And is it generally true that when multiple closed conducting surfaces enclose each other, the only one that acts as a Faraday cage is outermost one?