The Green operator $\Gamma ^{(n)}$ of the differential problem (having as eigenvalues the $\lambda _{h}^{(n)}$'s introduced in Nota I, is constructed. It is shown that the orthogonal invariant converges by decreasing to the corresponding orthogonal invariant $\mathcal{I}_{1}^{s} (\Gamma^{(n)})$ of the eigenvalue problem considered in Nota I and the approximation error is estimated.