Gender is social, constructed, ephemeral. Their sex didn't change, but the manifestations of their gender sure did. That's why males are males, but men are made. Sex is biology. Gender is the choices we assign based on biology.
Woman born male is someone making the choices of a woman born with a male sex.
She is not female, or making female choices, simply choices that we associate with females, and there is a difference. Female choices are menstruation, for example. Gender is transient, in the mind. Sex is permanent, in the body. We don't understand sex completely.