Al-‘Allaamah ibn ‘Uthaymeen:
What is the ruling regarding giving a sermon/speech when the dead are buried?
Speaking to people around you about death, being buried and similar things that soften the heart is a Sunnah transmitted from the Messenger of Allah - ﷺ. But to stand as a Khateeb [giving a sermon], this is not from the Sunnah.
Fatawa Nur ‘ala ad-Darb: 6/122
To this hour, I do not know that the Prophet - ﷺ - or one of the Sahabah stood giving a sermon to people like a Khutbah at the burial site.
Fatawa Nur ‘ala ad-Darb: 6/122
Al-‘Allaamah Saleh al-Fawzan:
Is it permissible for someone to stand at the grave site after someone has been buried and give a lecture or advise and remind his brothers? Has this been transmitted from the Prophet - ﷺ ?
This has not been transmitted from the Messenger - ﷺ -, except for one time, because the burial was not completely prepared, so he - ﷺ - sat down, and his companions sat around him and he advised them, but he did not continue to do so regularly. So whoever continuously does it is erroneous.
Whoever wants to advise people, then the Masajid are open and all praise is due to Allah, he can advise and teach the people about the same things at the grave.
Regarding giving sermons at the burial site, O noble Shaykh, are there any regulations concerning the burial that you may direct to the listeners?
Giving sermons at the burial site, if it is normal, such as a person sitting and waiting for the deceased to be buried; and speaks to his companions about things that would soften their hearts, then this is good. The prophet - ﷺ - did it.
But to stand as a Khateeb to the people then no, because this has not been transmitted that the Prophet - ﷺ - used to stand and give a sermon to the people after or during the burial. If this was legislated, the Messenger for Allah - ﷺ - would have been the first person to do so, and since he did not, it becomes known that it is not from the Sunnah.
However, a person who is sitting [waiting] and gives a speech/sermon to those sitting around him, it is not said that he is a Khateeb. Giving a sermon at the burial site does not necessitate that the person is a Khateeb. That is why it is incorrect to say that al-Bukhari, may Allah have mercy upon him, is of the opinion that a person can stand as a Khateeb and give a sermon to people, because he titled a chapter: Sermons During the Burial. He, may Allah have mercy upon him, didn’t title the chapter: Khutbahs at the Grave Site. And he distinguished between the two.
The point is, a person speaking to people around him about affairs related to death and being buried and so on to soften their hearts while he is waiting is a Sunnah that was transmitted from the Prophet - ﷺ, as for standing as a Khateeb then this is not from the Sunnah.
Fatawa Nur ‘ala ad-Darb: Tape # 351
This is an area of differing between the scholars and some have permitted it. However this seems to be the preponderant opinion as the evidence was explained. More Fatawa will be added on the subject InshaAllah.