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:
The phrase Sallu fi Rihalikum (Prayer at your camps) or Sallu fi Buyutikum (pray at your homes) added to the adhan is based on a narration attributed to Ibn Abbas.
During pandemics and in unexceptional circumstances, it is allowed for Muslims to offer the daily prayers and Friday prayer at home. Preserving the human soul is one of the objectives of the Shariah. We read in the Quran:
Because of that, We decreed upon the Children of Israel that whoever kills a soul unless for a soul or for corruption [done] in the land – it is as if he had slain mankind entirely. And whoever saves one – it is as if he had saved mankind entirely. And our messengers had certainly come to them with clear proofs. Then indeed many of them, [even] after that, throughout the land, were transgressors. (Al-Maidah 5:32)
Adhan (call to prayer) informs people about the time of prayer. Ibn Umar narrated that:
When the Muslims arrived at Madinah, they used to assemble for the prayer, and used to guess the time for it. During those days, the practice of Adhan for the prayers had not been introduced yet. Once they discussed this problem regarding the call for prayer. Some people suggested the use of a bell like the Christians, others proposed a trumpet like the horn used by the Jews, but Umar was the first to suggest that a man should call (the people) for the prayer; so Allah’s Messenger (peace be upon him) ordered Bilal to get up and pronounce the Adhan for prayers. (Al-Bukhari)
The reported formula of adhan is as follows. It was narrated that Abu Mahdhurah said:
The Messenger of Allah taught me the Adhan and said: ‘Allahu Akbar, Allahu akbar, Allahu Akbar, Allahu Akbar; Ashhadu an la ilaha illallah, Ashhadu an la ilaha illallah; Ashhadu anna Muhammadan Rasulallah, Ashhadu anna Muhammadan Rasulallah (Allah is the Greatest, Allah is the Greatest, Allah is the Greatest, Allah is the Greatest; I bear witness that there is none worthy of worship except Allah, I bear witness that there is none worthy of worship except Allah; I bear witness that Muhammad is the Messenger Allah, I bear witness that Muhammad is the Messenger Allah)’. Then he repeated it and said: ‘Ashhadu an la ilaha illallah, Ashhadu an la ilaha illallah; Ashhadu anna Muhammadan Rasulallah, Ashhadu anna Muhammadan Rasulallah; Hayya ‘alas-salah, Hayya ‘ala-salah; Hayya ‘alal-falah Hayya ‘alal-falah; Allahu Akbar, Allahu Akbar; La ilaha ill-Allah (I bear witness that there is none worthy of worship except Allah, I bear witness that there is none worthy of worship except Allah; I bear witness that Muhammad is the Messenger of Allah, I bear witness that Muhammad is the Messenger of Allah; Come to prayer, come to prayer; come to prosperity, come to prosperity; Allah is the Greatest, Allah is the Greatest; there is none worthy of worship except Allah).'” (An-Nasa`i)
With regard to the new formula of adding Sallu fi Rihalikum (Prayer at your camps) or Sallu fi Buyutikum (pray at your homes), there is nothing wrong with adding it to the adhan at times of pandemics and unexpected circumstances when it is very difficult for people to go to mosques to offer the five daily prayers and Friday prayer.
Muhammad bin Seereen narrated that: On a rainy day Ibn Abbas said to his muezzin, “After saying, ‘Ash-hadu anna Muhammadan Rasulullah’ (I testify that Muhammad is Allah’s Messenger), do not say ‘Haiya ‘Alas-Salat’ (come for the prayer) but say ‘Pray in your houses’.” (The man did so). But the people disliked it. Ibn Abbas said, “It was done by one who was much better than I (i.e. the Prophet (peace be upon him). No doubt, the Jumuah prayer is compulsory but I dislike to put you to task by bringing you out walking in mud and slush.” (Al-Bukhari)
Almighty Allah knows best.