  Greb\'ik and Rocha [Fractional Isomorphism of Graphons, Combinatorica 42, pp
365-404 (2022)] extended the well studied notion of fractional isomorphism of
graphs to graphons. We prove that fractionally isomorphic graphons can be
approximated in the cut distance by fractionally isomorphic finite graphs. This
answers the main question from ibid. As an easy but convenient corollary, we
deduce that every regular graphon can be approximated by regular graphs.
