Ruling of Making Du`aa before Finishing Prayer
It is highly recommended to make du`aa (invocation or supplication) after offering prayer and before making tasleem. Abu Hurairah (may Allah be pleased with him) narrated that the Messenger of Allah (peace be upon him) said: “When any one of you completes the last tashahhud. he should seek refuge with Allah from four (trials). I.e. from the torment of Hell, from the torment of grave, from the trial of life and death, and from the mischief of Masih Ad-Dajjal (Antichrist).” (Muslim)
However, making duaa after making tasleem at the end of prayer without raising one’s hands and without reciting it in unison is permissible. It was narrated that whenever the Messenger of Allah (peace be upon him) finished his Salah (prayer), he would beg forgiveness three times [by saying, ‘Astaghfirullah’ (3 times)] and then he would say: “Allahumma Antas-Salamu, wa minkas-Salamu, tabarakta ya Dhal-Jalali wal-Ikram. (O Allah! You are the Bestower of security and security comes from You; Blessed are You. O Possessor of glory and honor).” (Muslim)
To know more about the rulings of making duaa before and after tasleem in prayer, you could watch this short talk with Dr. Muhammad Salah.
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Source: Huda Youtube Channel.