  We investigate finite $\alpha '$ effects in string theory on a black hole
background. By explicitly computing tree level scattering amplitudes, we
confirm a duality between seemingly different states recently conjectured by
Giveon, Itzhaki, and Kutasov in [arXiv:1603.05822]. We verify that the relevant
3-point functions factorize in such a way that the duality between oscillator
and winding states becomes manifest. This leads to determine the precise
normalization of the dual vertex operators, and confirms at the level of the
interacting theory the identification of states suggested by the analysis of
the spectrum. This result implies a duality between two seemingly distinct
mechanisms driving the violation of the string winding number in the black hole
atmosphere.
