Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Using a cell phone during Friday Khutbah is not permissible. One should rather turn off his cell phone and give heed to the Friday sermon.
Answering your question, Dr. Muhammad Salama, PhD, Islamic Studies in English, Associate Professor at the Faculty of Islamic Sciences al-Madinah International University (Mediu), states:
It is obligatory upon those who attend Friday Prayer to listen attentively to the khateeb (one who delivers Friday sermon) and thus it is not permissible to engage in any idle activity.
Prophet Muhammad (peace be upon him) said, “He who touches pebbles, [during the Friday sermon] has engaged in idleness.” (Muslim)
It is even prohibited to give advice to another one as dictated by the prophetic declaration, ‘If you say to your fellow “Be quit”, while the imam is delivering the sermon on Friday, then you have engaged in idleness.’ (Al-Bukhari and Muslim)
Accordingly, using one’s cell phone during Friday Khutbah is similarly prohibited. One should rather turn off his cell phone and give heed to the sermon.
Almighty Allah knows best.