  This paper is dedicated to the rigorous numerical analysis of a Multiscale
Finite Element Method (MsFEM) for the Stokes system, when dealing with highly
heterogeneous media, as proposed in [B.P.~Muljadi et al., arXiv:1404.2837]. The
method is in the vein of the classical Crouzeix-Raviart approach. It is
generalized here to arbitrary sets of weighting functions used to enforced
continuity across the mesh edges. We provide error bounds for a particular set
of weighting functions in a periodic setting, using an accurate estimate of the
homogenization error. Numerical experiments demonstrate an improved accuracy of
the present variant with respect to that of Part I, both in the periodic case
and in a broader setting.
