  In this article we study the decoupling structure and multipoint moment of
the inverse of the Gaussian multiplicative chaos. It is also the second part of
preliminary work for extending the work in "Random conformal weldings" (by K.
Astala, P. Jones, A. Kupiainen, E. Saksman) to the existence of Lehto welding
for the inverse. In particular, we prove that the dilatation of the inverse
homeomorphism on the positive real line is in $L^{1}([0,1]\times[0,2])$.
