Is it permissible for women to pray in a place lower than that of the Imam, while the sound reaches them via loudspeakers?

It is permissible for the congregant to follow the Imam upon merely hearing the takbir, if the congregant is inside the mosque. It is not a condition to see the Imam or the congregants. Therefore, the prayer of women in the mosque is valid even if they are in a lower place than the Imam.

Scholars have differed on the authenticity of the hadith prohibiting the Imam from being elevated above the congregant. It has been interpreted as applying only if the Imam prays alone in an elevated place.

The author of the text holds that prayer behind an Imam who is elevated above the congregants is valid, but disliked if the elevation is a cubit or more. Sheikh Ibn Uthaymeen adduced the Prophet's (peace be upon him) prayer on the minbar as evidence for the validity of such a prayer.

The second opinion is that there is no dislike for the Imam's elevation whatsoever, due to the weakness of the hadith used by the companions as evidence. Some scholars have restricted the issue to cases where the Imam is not isolated in his place, in which case there is no dislike.

If the congregant is in a higher place, it is not disliked, and similarly, if the Imam is below and the congregants are above him.

If the hadiths prohibiting the Imam's elevation are authentic, then the disliked aspect is removed in cases of necessity. This applies to people praying on different floors due to space constraints.