  A recent paper [R22] established "Frobenius reciprocity" as a bijection $t$
between certain symplectically reduced spaces (which need not be manifolds),
and conjectured: 1{\deg}) $t$ is a diffeomorphism when these spaces are endowed
with their natural subquotient diffeologies, 2{\deg}) $t$ respects the reduced
diffeological $2$-forms they may (or might not) carry. In this paper, we prove
both this conjecture and a similar one on prequantum reduction, and also give
new sufficient conditions for the reduced forms to exist. We stop short of
proving that they always exist.
