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 one-dimensional field redefinitions and total derivative terms, they are invariant under the $O(9,9)$ transformations.

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