  Recently, imposing the $O(1,1)$ symmetry on the circle reduction of the
classical effective action of string theory, we have found all NS-NS couplings
of type II superstring theories at order $\alpha'^3$. In this paper we use the
cosmological reduction on the couplings and show that, up to field
redefinitions and total derivative terms, they are invariant under the $O(9,9)$
transformations.
