This paper is a sequel to [9]. Its goal is to verify that the virtual top Chern class c 1/r in the Chow group of the moduli space of higher spin curves $$\overline M _{{g,n}}^{{1/r}} $$ constructed in [9], satisfies all the axioms of spin virtual class formulated in [5]. Hence, according to [5], it gives rise to a cohomological field theory in the sense of Kontsevich-Manin [7]. As was observed in [9], the only non-trivial axioms that have to be checked for the class c 1/r are two axioms that we call Vanishing axiom and Ramond factorization axiom. The first of them requires c 1/r to vanish on all the components of the moduli space $$\overline M _{{g,n}}^{{1/r}} $$ where one of the markings is equal to r - 1. The second demands vanishing of the push-forward of c 1/r restricted to the components of the moduli space corresponding to the so called Ramond sector, under some natural finite maps.