What is authentically established immediately after the farḍ prayer is dhikr, not a collective supplication: saying "Astaghfirullāh" three times, then "Allāhumma anta as-Salām wa minka as-salām, tabārakta yā Dhā al-Jalāli wa'l-Ikrām" (Ṣaḥīḥ Muslim, Kitāb al-Masājid, from Thawbān); "Lā ilāha illa-llāhu waḥdahu lā sharīka lah, lahu'l-mulku wa lahu'l-ḥamd, wa huwa ʿalā kulli shay'in qadīr..." (Sahih al-Bukhari 844, from al-Mughīrah ibn Shuʿbah); the tasbīḥ, taḥmīd and takbīr (Sahih al-Bukhari 843); and the two muʿawwidhāt (Sunan Abi Dawud 1523, from ʿUqbah ibn ʿĀmir, graded ṣaḥīḥ). Nothing authentic reports that the Prophet (ﷺ) and his Companions habitually raised their hands together in one voice after every farḍ prayer, which is why Ibn Taymiyyah, Ibn Bāz and Ibn ʿUthaymīn held that taking it as a regular practice is an innovation. There is legitimate difference here: some scholars permitted it occasionally or for a particular need, and a person making his own quiet supplication after the prayer is not doing anything blameworthy in itself. The Sunnah-consistent place for personal dua within the prayer is before the salām, after the tashahhud (Sahih al-Bukhari 835), and Allah says, "Call upon your Lord in humility and privately" (Quran 7:55).
Q&A · Dua & Dhikr
Is the congregational dua with raised hands after the obligatory prayers a Sunnah?
Evidence — the daleel
Quran 7:55Sahih al-Bukhari 844 ṢaḥīḥSahih al-Bukhari 843 ṢaḥīḥSunan Abi Dawud 1523Sahih al-Bukhari 835 Ṣaḥīḥ
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Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.