Is it permissible for a Haafizah to lead only women in Taraaweeh.

Answer

It is not permissible for a woman to lead even women in Taraaweeh Salaat. The objective of Taraaweeh is not to 'strengthen' Hifz. The objective is to gain Allah's Pleasure by means of humbly fulfilling the obligation. The Shariah urges women to perform Salaat alone and in privacy. Performing Salaat in seclusion and solitarily increases her proximity to Allah Ta'ala.