  We give a proof of the LMO conjecture which say that for any simply connectd
simple Lie group $G$, the LMO invariant of rational homology 3-spheres recovers
the perturvative invariant $\tau^{PG}$. By Habiro-Le theorem, this implies that
the LMO invariant is the universal quantum invariant of integral homology
3-spheres.
