All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The scholars of Hadeeth classified the narration which is reported about “the prayer for a need” [Salat Al-Haajah] as a Dha’eef narration. However, many jurists are of the view that this prayer is desirable based on this narration, as we clarified in Fataawa 84048 and 82384.
Nonetheless, even according to the view that this prayer is desirable, it is not mentioned in the narration that it should be performed in congregation. Therefore, performing this prayer in congregation immediately after the Friday prayer, especially if this is on a regular basis, is considered an added religious innovation even if the prayer itself is permissible in principle (as this is an innovative way of performing it).
The prayers which are permitted to be performed in congregation are the five obligatory prayers, the Friday prayer, the funeral prayer, the 'Eed prayer, the prayer imploring for rain, the Taraweeh prayers, the prayer because of fear, and the eclipse prayer.
As regards the prayer for need in the manner which is mentioned in the question, it is considered as an added religious innovation.