The aim of this second part is to compute explicitly the Lusztig restriction of the characteristic function of a regular unipotent class of a finite reductive group, improving slightly a theorem of Digne, Lehrer and Michel. We follow their proof but introduce new information, namely the computation of morphisms $\varphi_{L,v}^G$ defined in the first part when $v$ is a regular unipotent element. This new information is obtained by studying generalizations of the variety of companion matrices which were introduced by Steinberg.