  In the supersymmetric left-right model, the light neutrino masses are given
by the Type-II seesaw mechanism. A duality property about this mechanism
indicates that there exist eight possible Higgs triplet Yukawa couplings which
result in the same neutrino mass matrix. In this paper, We work out the
one-loop renormalization group equations for the effective neutrino mass matrix
in the supersymmetric left-right model. The stability of the Type-II seesaw
scenario is briefly discussed. We also study the lepton-flavor-violating
processes ($\tau\to \mu\gamma$ and $\tau\to e\gamma$) by using the
reconstructed Higgs triplet Yukawa couplings.
