Hurwitz-orbit conjecture for factorizations in well-generated complex reflection groups

Let $W$ be a well-generated finite complex reflection group, let $c$ be a Coxeter element of $W$, and consider factorizations of $c$ into reflections. Two such reflection factorizations share the same multiset of conjugacy classes when the multisets of conjugacy classes of their factors coincide. Hurwitz-orbit conjecture. Two reflection factorizations of $c$ lie in the same Hurwitz orbit if and only if they share the same multiset of conjugacy classes. This is presented as a verbatim generalization of the theorem for finite real reflection groups; its status for well-generated finite complex reflection groups is not resolved in the supplied text.