  In this paper we prove that for Gromov-Witten theory of $P^1$ orbifolds of
ADE type the genus-2 G-function introduced by B. Dubrovin, S. Liu, and Y. Zhang
vanishes. Together with our results in [LW], this completely solves the main
conjecture in their paper [DLZ]. In the process, we also found a sufficient
condition for the vanishing of the genus-2 G-function which is weaker than the
condition given in our previous paper [LW].
