An effective non-redundant near-field to far-field transformation (NFTFFT) with spherical scan, which accounts for the offset mounting of a quasi-planar antenna and employs the same number of NF data as in the case of onset mounting, is developed in this paper. The interest for this NFTFFT arises from the fact that the mounting where the antenna and the measurement sphere centers coincide could result to be impracticable. In this case, the amount of NF data required by the traditional spherical NFTFFT can significantly increase. In the proposed NFTFFT, this drawback has been overcome by accurately recovering these NF data from the collected non-redundant ones via a sampling expansion, obtained by exploiting the non-redundant sampling representations and assuming the antenna as enclosed in an oblate spheroid. Numerical and experimental results assessing the effectiveness of the developed technique are reported.