All perfect praise be to Allah, The Lord of the Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
In order for following the Imam to be valid, it is conditioned that prayer performers, be they inside or outside the Masjid, are aware of the Imaam`s movements through hearing his Takbeer, seeing him or seeing those praying behind him. Al-Imam An-Nawawi(May Allah have mercy on him) said, "In order for following the Imam to be valid, it is conditioned that those led in prayer are aware of his movements, whether all were in a Masjid or any other place of prayer, as agreed by Shafie scholars. Moreover, fellow Shafie scholars said: "This can be achieved through hearing the Imaam or those praying behind him or seeing their movement. They have also agreed on the permissibility of relying on any of these acts."{Al-Majmou`, 4/201}.
As keeping track of the Imaam`s movements in prayer is among the conditions for the validity of following him, the screen, which is to be placed in the women`s prayer place, serves that end. Therefore, it could play an important role ; particularly, when the Imaam performs the Sujud of Quranic recital or Sujud As-Sahw (Forgetfulness prostration) since those who could only hear him may think that he made the Takbeer for moving from standing up to bowing.
In conclusion, the screen is a means of keeping up with the movements of the Imaam and doesn`t violate Sharia since it merely displays him. However, it is preferable that praying people don`t busy themselves with it, save for a valid need, in order not to be distracted from their prayer or lose submissiveness. And Allah knows best.