In measurement scenarios with ground planes the boundary condition has to be included appropriately in the near-field to far-field transformation. For spherical near-field antenna measurements, techniques exist to include a ground plane in the xy-plane (z = 0m). In this paper, we will describe a transformation procedure including a translation of the transformation origin, so that the ground plane can be at any height ζ to overcome that limitation of existing techniques. The procedure is demonstrated by a simulation and measurement example.