If a magnet is put inside one coil of wire a voltage is produced. What will happen if the magnet is put inside two coils of wire?

I would expect a voltage in both coils of wire.Note that, if the two coils are connected, the voltages (and corresponding currents) in the coils can interact.

Also, if the two coils are NOT connected, they can STILL interact, since a current will produce its own magnetic field.