  We prove a converse of Fatou type result for certain eigenfunctions of the
Lalplace-Beltrami operator on Harmonic NA groups relating sectorial convergence
and admissible convergence of Poisson type integrals of complex (signed)
measures. This result extends several results of this kind proved eariler in
the context of the classical upper half space $\mathbb{R}_+^{n+1}$. Similar
results are also obtained in the degenerate case of the real hyperbolic spaces.
