Uniform closures of fourier-stieltjes algebras

Let H be a closed normal subgroup of a locally compact group G. Assume that f is a continuous function on G such that it is constant on the cosets of H in G and it can be approximated uniformly by coefficient functions of unitary representations of G. We show that f can be approximated uniformly by coefficient functions of representations of G which are lifted from unitary representations of G/H. For abelian G, our theorem is a conjecture of R. B. Burckel.