In the previous papers of this series, we introduced the implicit integral method (IIM) to solve those radiative transfer (RT) problems in which the source function depends on an integral of the specific intensity of the radiation field over directions and frequencies. The IIM rests upon a forward-elimination, back-substitution scheme naturally based on the physics of the RT process, and does not require any matricial algorithm. Customary methods to solve RT problems, in which the source function depends on the aforesaid integral, rest upon matrix algorithms. In spherical geometry, due to the strong anisotropy of the radiation field brought about by the limb curvature, the so-called peaking effect, the number of directions necessary to describe this anisotropy is exceedingly high, and consequently the relevant matrices are hard to handle. The present paper deals with the application of the IIM to RT problems in spherical geometry, where the distinctive nonmatricial character of the method can be fully exploited, given the intrinsic high dimensionality of the problem.