Boundary states, extended symmetry algebra, and module structure for certain rational torus models J. Math. Phys. 43, 6085 (2002) We continue the study of hidden Z 2 symmetries of the four-point sl͑2͒ k KnizhnikZamolodchikov equation initiated by Giribet ͓Phys. Lett. B 628, 148 ͑2005͔͒. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sector = 1 is involved. We give a formula that shows how this observable can be expressed in terms of the four-point function of non spectral flowed states. This means that the formula holding for the winding violating four-string scattering processes in AdS 3 has a simple expression in terms of the one for the conservative case, generalizing what is known for the case of three-point functions, where the violating and the nonviolating structure constants turn out to be connected one to each other in a similar way. What makes this connection particularly simple is the fact that, unlike what one would naively expect, it is not necessary to explicitly solve the five-point function containing a single spectral flow operator to this end. Instead, nondiagonal functional relations between different solutions of the Knizhnik-Zamolodchikov equation turn out to be the key point for this short path to exist. Considering such functional relation is necessary but it is not sufficient; besides, the formula also follows from the relation existing between correlators in both Wess-Zumino-Novikov-Witten ͑WZNW͒ and Liouville conformal theories.