  Non-factorizable virtual corrections to Higgs boson production in weak boson
fusion at next-to-next-to-leading order in QCD were estimated in the eikonal
approximation [1]. This approximation corresponds to the expansion of relevant
amplitudes around the forward limit. In this paper we compute the leading power
correction to the eikonal limit and show that it is proportional to first power
of the Higgs boson transverse momentum or the Higgs boson mass over partonic
center-of-mass energy. Moreover, this correction can be significantly enhanced
by the rapidity of the Higgs boson. For realistic weak boson fusion cuts, the
next-to-eikonal correction reduces the estimate of non-factorizable
contributions to fiducial cross section by O(30) percent.
