  We show that the higher rank triplet W-algebra is simple when p is bigger
than or equal to h-1. Furthermore, we show that the Feigin-Tipunin's module
over the higher rank triplet W-algebra introduced in arXiv:1002.5047 is simple
if the parameter is in the closure of the fundamental alcove, and give the
decomposition as a direct sum of simple modules over the affine W-algebras at
level p-h.
