We continue the study of equivalent boundary conditions in ferromagnetic domains crossed by a thin split. In this second part, we add nonhomogenous boundary conditions arising from interactions such as surface anisotropy and super-exchange. We expand the problem up to the first order and establish equivalent boundary conditions in presence of surface anisotropy and super-exchange. In particular, the well-posedness of the expansion problem with equivalent boundary condition and the convergence in some meaning of the expansion are proven.