  The case of non-zero momentum level reduction in Wiener path integrals for a
mechanical system with symmetry describing the motion of two scalar particles
with interaction on a Riemannian product manifold with the given action a
compact semisimple Lie group is considered. The original product manifold
consists of the vector space and a smooth compact finite-dimensional Riemannian
manifold, which, due to the action of the group, can be regarded as the total
space of the principal fiber bundle. The integral relation between the path
integrals representing the fundamental solutions of the backward Kolmogorov
equation defined on the total space of the principal fiber bundle (the original
Riemannian product manifold) and the corresponding backward Kolmogorov equation
gion the space of the sections of the associated covector bundle is obtained.
