We extend a previous sharp upper bound of the first strong stability eigenvalue due to Alías et al.  for the context of closed submanifold immersed with nonzero parallel mean curvature vector field in the Euclidean sphere and, through this result, we obtain a new characterization for the Clifford torus.
 L.J. Alías, A. Barros and A. Brasil Jr., A spectral characterization of the H(r)-torus by the first stability eigenvalue, Proc. Amer. Math. Soc. 133 (2005), 875–884.