  We derive from the compatibility of associators with the module harmonic
coproduct, obtained in Part I of the series, the inclusion of the torsor of
associators into that of double shuffle relations, which completes one of the
aims of this series. We define two stabilizer torsors using the module and
algebra harmonic coproducts from Part I. We show that the double shuffle torsor
can be described using the module stabilizer torsor, and that the latter torsor
is contained in the algebra stabilizer torsor.
