All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the written Friday sermon includes its pillars, like praising Allaah, exalting the mention of the Prophet reciting a verse from the Quran and admonishing people to fear Allaah, then it is permissible to read this sermon, even if it was written by a woman.
In principle a Friday sermon should not be read; however, if one reads it from a prepared paper then it is permissible if it meets the afore-mentioned conditions.
We do not know of any scholar who stated that for the Friday speech to be valid it should be written by a man. In addition to this, a woman writing a Friday sermon for a man is considered as consultation. Indeed, it is confirmed in the Sunnah that it is permissible to act according to the consultation of a woman.
For instance, the Prophet acted according to the consultation of Um Salamah in relation to Al-Hudaybiyah peace treaty. The Prophet ordered the Companions to slaughter their sacrifice and shave their head but none of them did so. He repeated this three times, but no one acted according to his order, [Not because they wanted to disobey him but] because they were very keen and willing to perform 'Umrah - since they came from Madeenah in a state of Ihraam but the people of Makkah did not allow them to enter it]. So the Prophet entered to Um Salamah and told her what happened. She told him: "Do you want them to do what you ordered them? Go out and do not talk to anyone of them until you slaughter your sacrifice and shave your head…." [So when the Prophet acted according to her advice, all the Companions imitated him] [Al-Bukhari]
Therefore, it is permissible to act according to the advice of a wise woman.
Finally, we advise you to fear Allaah and not scatter and divide into sects and groups because division is evil as Ibn Mas'ood said. Division also leads to hating each other and you are in a country where you need to unite upon the truth and calling people to Allaah. So be careful of dividing into sects and groups and be brothers in Islam.
Allaah Knows best.