As salaamu alaikum
Please is it permissible for the Mu'athin or any other person among the ma'mum to say 'sallu alan Nabiyi Kareem' and the rest will say 'salla Allahu alaihi wa sallim' immediately after tasleem?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, is His slave and Messenger.

Invoking peace and blessings upon the Prophet is permissible at all times, and its most confirmed time is at the end of the Prayer before reciting the Tasleem. It is required of a Muslim to often invoke peace and blessings upon the Prophet . However, it is not an act of the Sunnah for the Imam, Mu’aththin (the one raising the Athaan, call to prayer), or others to command the worshippers to invoke peace and blessings on the Prophet after finishing each Prayer.

Doing this regularly falls under the category of Bid‘ah (religious innovation) because it gives the impression that it is prescribed to invoke peace and blessings upon him at that particular time and that it is part of the Sharee‘ah. However, the Sharee‘ah does not prescribe invoking peace and blessings on the Prophet at that time in particular.

The Prophet encouraged the Muslims to recite a set of Athkaar after the Prayer, but they do not include the command to invoke peace and blessings upon him or reciting it out loud or collectively. None of these practices were prescribed under the Sharee‘ah. The Prophet said: “Whoever introduces into this matter of ours (i.e. Islam) that which is not a part of it will have it rejected.” [Al-Bukhari and Muslim] The version cited in Saheeh Muslim states: “Whoever does any action that is not in accordance with this matter of ours (i.e. Islam) will have it rejected.” Imam An-Nawawi said: “This Hadeeth is one of the great principles of Islam and an example of the succinct statements of the Prophet . It is an explicit statement about rejecting all (religious) innovations ... This Hadeeth should be memorized and used in invalidating wrong practices and should be widely used as proof in this regard.” [End of quote]

Allah Knows best.