We conduct an investigation of the global structure of Kerr-Newman-BR spacetime and its various subcases such as Schwarzschild-BR spacetime. In this work, we extend the result of our previous studies, where we found that $r\to \infty$ is not the proper conformal infinity. By using the reciprocal coordinate y = 1/r, we show that the whole family of Kerr-Newman-BR spacetimes can be continuously extended through the surface$r\to \infty$. However, the conformal structure after passing $r\to \infty$ strongly depends on the type of spacetime one is considering (either rotation is present, or not) and on the polar direction one chooses to be fixed (namely, whether we consider generic polar angle $\theta$, or we focus on the behaviour near the equatorial plane $\theta =\pi /2$, or near the poles $\theta =0,\pi$). Physically this extension can be interpreted as kind of "confinement box", created solely by the magnetic field. Finally, we discuss the universality of such a continuous extension.