  Cloaking of static magnetic fields by a finite thickness type-II
superconductor tube surrounded by a coaxial paramagnet shell is studied. On the
basis of exact solutions to the London and Maxwell equations, it is shown that
perfect cloaking is realizable for arbitrary geometrical parameters including
the thin film case for both constituents. In contrast to previous approximate
studies assuming perfect diamagnetism of the superconductor constituent, it is
proven that cloaking provides simultaneously full undetectability, that is the
magnetic moment of the structure completely vanishes as well as all high-order
multipole moments as soon as the uniform field outside remains unaffected.
