The (electromagnetic) generalized Lorenz–Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz–Mie theory which deals with the simpler case of a plane wave illumination. In a recent paper, we consider (i) elastic cross-sections in electromagnetic generalized Lorenz–Mie theory and (ii) elastic cross-sections in an associated quantum generalized Lorenz–Mie theory. We demonstrated that the electromagnetic problem is equivalent to a superposition of two effective quantum problems. We now intend to generalize this result from elastic cross-sections to inelastic cross-sections. A prerequisite is to build an asymptotic quantum inelastic generalized Lorenz–Mie theory, which is presented in this paper.