Is it prescribed to call the people via loudspeakers by saying “as-salaatu jaami‘ah (prayer is about to begin)”?.
It is not prescribed to give the call via loudspeakers for worshippers to assemble for the funeral prayer, whether that is by saying “as-salaatu jaami‘ah (prayer is about to begin)” or saying “as-salaatu ‘ala al-mayyit (prayer for the deceased)”.
For more information please see the answer to question no. 6008
Al-Bahooti (may Allah have mercy on him) said: No call should be given for the funeral prayer or Taraweeh, because that is an innovation. Even worse than that is what is done at the funeral prayer of reciting poetry or mentioning characteristics, most of which may be lies. In fact that comes under the heading of wailing for the dead.
End quote from Kashshaaf al-Qinaa‘, 1/234
Imam ash-Shaafa‘i (may Allah have mercy on him) said: “… With regard to the funeral prayer and all naafil prayers apart from Eid prayer and the eclipse prayer, there is no adhaan (call to prayer) for them or call by saying “as-salaatu jaami‘ah (prayer is about to begin)”.
End quote from Sharh al-Muhadhdhab, 3/83
In al-Mawsoo‘ah al-Fiqhiyyah (16/7) it says: In ash-Sharh as-Sagheer it says: It is makrooh to shout in the mosque or at its door, saying, “So and so has died, hasten to his funeral!” However, announcing it in a low voice without shouting is not makrooh. End quote.
As-San‘aani (may Allah have mercy on him) said: His saying in ash-Sharh, that it is mustahabb when calling people to prayer on Eid and other occasions when it is not prescribed to give the adhaan, such as the funeral prayer, to say “as-salaatu jaami‘ah (prayer is about to begin)”, is not correct, because there is no evidence to suggest that it is mustahabb. If it were mustahabb, the Prophet (blessings and peace of Allah be upon him) would not have omitted to do it, and neither would the Rightly Guided Caliphs after him. Yes, that is proven in the case of the eclipse prayer, but it is not proven in other cases and it is not valid to draw an analogy, because if the same reason existed in his time but he did not do it, doing it after his time is an innovation. So it is not correct to affirm it on the basis of analogy or otherwise.
End quote from Subul as-Salaam, 1/184
And Allah knows best.