The stronger position regarding supplication after the prayer is that it should be before the closing salam
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Is it better in the supplication: (O Allah, help me to remember You, give thanks to You, and worship You in the best manner) should it be before the salam or after the salam, or is it better to do it in both places?
It is better to do it before the salam, because that is how it was reported in some narrations, and because supplication is done before the salam, as in the hadith of Ibn Mas'ud when he mentioned the tashahhud, he said: (then let him choose whatever supplication he wishes) and based on this, he says: (O Allah, help me to remember You, give thanks to You, and worship You in the best manner) before he says the salam. And after the salam, what did Allah say? [Al-Nisa: 103] He did not say: so call upon Him.
And as for the saying of the one praying when he says the salam: I seek forgiveness from Allah, three times. This is because the purpose of this seeking forgiveness is to patch up any deficiency that occurred in the prayer, so it is appropriate for it to be done immediately after the salam.
It is better to do it before the salam, because that is how it was reported in some narrations, and because supplication is done before the salam, as in the hadith of Ibn Mas'ud when he mentioned the tashahhud, he said: (then let him choose whatever supplication he wishes) and based on this, he says: (O Allah, help me to remember You, give thanks to You, and worship You in the best manner) before he says the salam. And after the salam, what did Allah say?
Then when you have completed the prayer, remember Allah
فَإِذَا قَضَيْتُمُ الصَّلاةَ فَاذْكُرُوا اللَّهَAnd as for the saying of the one praying when he says the salam: I seek forgiveness from Allah, three times. This is because the purpose of this seeking forgiveness is to patch up any deficiency that occurred in the prayer, so it is appropriate for it to be done immediately after the salam.