If someone came late to join the funeral prayers, how should he complete those Takbirs that he missed and what should he recite in them?
If there is concern that the Janaza shall be carried away, then the person who came late should hastily say the Takbirs without making any Du’a and then make the Salam. Otherwise, (if there is no such concern), then the Takbirs should be said in order and the Du’as prayed respectively. For example, if he missed three Takbirs, then after having said the fourth Takbir with the Imam (afterwhich the Imam and the rest will do the Salam), he should say the first Takbir and then pray Thana, then say the second Takbir and pray Durud, then the third and make the Du’a. If two Takbirs are missed, then in the third Takbir which he said with the Imam he shall make Du’a, thereafter the Imam shall make Salam. After the Salam, he shall say the first Takbir, afterwhich he should pray Thana and after the second, he should pray Durud and thereafter make the Salam. If he only missed one Takbir, then after the Salam, he should pray one Takbir after which he should pray Thana. Thereafter he should make the Salam himself.
And Allah ﷻ knows the best
Imam Ahmad Rida Khan رحمة الله تعالى عليه
Translation by Dr Musharraf Hussain Al-Azhari Translator of Majestic Quran, www.majesticquran.co.uk