  In this work, we study the well-posedness of the three dimensional
magneto-hydrostatic equation under Grad-Rubin boundary value conditions. The
proof relies on a fixed point argument to construct solutions to an
elliptic-hyperbolic problem in a perturbative regime by means of
pseudo-differential operators with symbols with limited regularity in H\"older
spaces. As a byproduct, the employed technique in this work is more flexible
and simplifies the arguments of the proof for the previous two-dimensional
setting.
