We wash the dead body, perform funeral (janazah) prayer, bury the dead body in a grave and throw three fistful of soil and then fill the grave.
But what is the funeral procedure like if the body is not found?
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When the body of the deceased is not present, funeral prayers may be offered in absentia in exactly the same manner (the four takbirat) as if the body was present. All the other tasks that can only be performed if the body of the deceased is present may be skipped.
Multiple authentic hadiths show that the Prophet (ﷺ) performed the funeral prayers (Arabic: صلاة الجنازة, salat al-janaza) in absentia on Armah the Negus (Arabic: النجاشي أصحمة بن أبجر, Al-Najashi), the king of Abyssinia (Arabic: الحبشة) during the time of the first and second hijra to Abyssinia. For example:
حَدَّثَنِي عَبْدُ اللَّهِ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا يَزِيدُ، عَنْ سَلِيمِ بْنِ حَيَّانَ، حَدَّثَنَا سَعِيدُ بْنُ مِينَاءَ، عَنْ جَابِرِ بْنِ عَبْدِ اللَّهِ ـ رضى الله عنهما أَنَّ النَّبِيَّ صلى الله عليه وسلم صَلَّى عَلَى أَصْحَمَةَ النَّجَاشِيِّ، فَكَبَّرَ عَلَيْهِ أَرْبَعًا. تَابَعَهُ عَبْدُ الصَّمَدِ
Narrated Jabir bin 'Abdullah: The Prophet (ﷺ) offered the funeral prayer for Ashama, the Negus, with four Takbir.
There are numerous other hadiths to the same effect in Sahih Al-Bukhari (hadiths 63/103, 23/75, 23/9), Sahih Muslim (hadiths 32/92, 11/82), Muwatta' Malik (hadith 505360), Sunan An-Nasa'i (hadiths 21/158, 21/154, 21/164). All these hadiths prove that funeral prayers in absentia (Arabic: صلاة الجنازة على الغائب) are permitted.
Some followers of the Shafe'i and Hanbali schools allow funeral prayers in absentia with no conditions (Ref: Al-Moghni, Vol.2, p. 382, Q. 1605, by Ibn Qudamah; Arabic: المغني). However, Ahmad ibn Hanbal put conditions on funeral prayers in absentia:
Similarly, some of the Shafe'i school followers have a condition that the funeral prayers in absentia be offered on the same day of death by relatives of the deceased (Ref: Asna Al-Matalib, Vol. 1, p. 322; Arabic: أسنى المطالب في شرح روض الطالب).
Some of the Maliki and Hanafi schools followers say that performing funeral prayers in absentia is only permissible to the Prophet (ﷺ) (Ref: Bada'e Al-Sana'e, Vol. 1, p. 312; Arabic: بدائع الصنائع في ترتيب الشرائع). The majority of scholars (Arabic: الجمهور), including followers of Maliki and Hanafi schools do not agree as the rule is what the Prophet (ﷺ) did is permissible to all the Muslims to do, except when there is a verse (Qur'an or hadith) that limit the permissibility to the Prophet (ﷺ).
ذكرنا أن مذهبنا جوازه ومنعها أبو حنيفة . دليلنا حديث النجاشي وهو صحيح لا مطعن فيه وليس لهم عنه جواب صحيح
We mentioned that: Our madhhab is that funeral prayers in absentia is permitted, and Abu Hanifa did not allow it. Our evidence are the hadith about the Negus, and it is authentic, and they [Hanafis] do not have a valid response [why it is not permitted].
— NOTE: My own translation, so treat with care.
You can remember anyone's death, commemorate it as Rasulullah ﷺ has taught us.
As you have questioned, and also mentioned in your comment about the answer given by Darul Ifta Birmingham, there is no prayers named salat-al-janazah-al-ghaib.
So, if anyone's body is lost whether it is by drowning, burning or any other way, you can make dua for him, make sadaqah for him, pray for his forgiveness.
But there is no funeral acts in this case.
Allah knows the best.