In this teshuva, Rav Moshe tackles both the issue of hearing Megilla via microphone as well as the issue of the status of men relative to that of women vis-a-vis reading the Megilla. The question came from a girls school in Gadera which apparently had an overflow problem and wanted to use a microphone to enable all of its students to hear the Megilla.
In response, Rav Moshe wrote that it would be better to have a delay after Maariv in order to clean out the cafeteria and then use both the Beit Midrash and the cafeteria as staging locations for concurrent Megilla readings, rather than use a microphone. He further notes that both locations should have a minyan of men, but rejects the notion that men are "adif" (lit. "better") than women when it comes to hearing the Megilla, as both are equally obligated in this mitzva.
[I will note that on that last point, Rav Moshe does not get into the issue of women reading the Megilla at all - he seems to not consider that as an option.]