What do the experts and scholars of shari’ah say regarding how a latecomer should complete the funeral prayer?
If the latecomer fears that the deceased body will be removed immediately, then he should say the Takbirs without reciting anything in between. If there is no fear of the deceased body being removed immediately, he should offer the funeral prayer in the correct order. For instance, if he joined the Imam in the fourth Takbir, then after the Imam has offered Salam, the latecomer should say the first Takbir and recite Thana, then say the second Takbir and recite Durud Sharif. If he only missed the first Takbir, then after the Salam, he should offer the first Takbir and say Thana.
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