If a woman intended to perform ghusl to cleanse herself from menstruation, but then forgot her intention during the ghusl and performed a normal ghusl, is that sufficient?

The intention for ghusl (definition) (ritual bath) is not invalidated if it precedes the entry into the bath by a short time. However, if there is a long separation between the intention and the commencement of ghusl, the ghusl becomes invalid due to the absence of the intention. As for forgetting the intention after it has been made in its proper place, this does not invalidate the ghusl, because continuously recalling the intention is not a condition. Rather, the condition is the continuity of its ruling, meaning that the person does not intend to nullify it.