Is Dua after Fard prayer accepted? Is Dua after Khatam Quran accepted?

Yes, there is a Hadith mentioning that Dua (supplication) after Fard prayer is accepted. The same Hadith affirms that Dua after Khatam (completing) Quran is accepted. The Hadith is weak. However, weak Hadith can be used for such matters.

عَنِ الْعِرْبَاضِ بْنِ سَارِيَةَ قَالَ: قَالَ رَسُولُ اللهِ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ: مَنْ صَلَّى صَلَاةَ فَرِيضَةٍ فَلَهُ دَعْوَةٌ مُسْتَجَابَةٌ، وَمَنْ خَتَمَ الْقُرْآنَ فَلَهُ دَعْوَةٌ مُسْتَجَابَةٌ

From (Sayidina) al-Irbaad bin Sariyah (May Allah Most High be pleased with him) who said, the Messenger of Allah ﷺ said, ‘Whoever prays an obligatory prayer has an accepted Dua. And whoever completes (Khatm) the (Holy) Quran has an accepted supplication.’ (al-Tabarani, al-Mojam al-Kabeer, 647).

The Hadith above states that Dua (supplication) after Fard prayer is accepted, and Dua after Khatam (completing) Quran is accepted too. However the Hadith is weak according to Imam al-Haythami and others. Since the Hadith is weak, we cannot categorically affirm that the holy Prophet ﷺ said these words. However, there is a possibility or probability that the Prophet ﷺ made these statements. Therefore, weak Hadith are not rejected. Nor are they treated like Sahih Hadith. (See the links below for more details).

عَنِ الْعِرْبَاضِ بْنِ سَارِيَةَ قَالَ: قَالَ رَسُولُ اللَّهِ – صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ -: «مَنْ صَلَّى صَلَاةَ فَرِيضَةٍ فَلَهُ دَعْوَةٌ مُسْتَجَابَةٌ، وَمَنْ خَتَمَ الْقُرْآنَ فَلَهُ دَعْوَةٌ مُسْتَجَابَةٌ». رَوَاهُ الطَّبَرَانِيُّ، وَفِيهِ عَبْدُ الْحَمِيدِ بْنُ سُلَيْمَانَ وَهُوَ ضَعِيفٌ

From (Sayidina) al-Irbaad bin Sariyah (May Allah Most High be pleased with him) who said, the Messenger of Allah ﷺ said, ‘Whoever prays an obligatory prayer has an accepted Dua. And whoever completes (Khatm) the (Holy) Quran has an accepted supplication.’ (al-Tabarani, al-Mojam al-Kabeer, 647). Narrated by al-Tabarani, and it has Abd al-Hameed bin Sulaymaan (in the chain). And he is weak. (Imam Noorud-deen al-Haythami, Majma’ al-Zawaid).

And Allah Most High Knows Best.

-Answered by Shaykh Noorud-deen Rashid (06.05.2022)

See also:
What do the different Hadith classification terms mean?
Using weak Hadith.

Hadith about making dua for khatam al Quran

Is there evidence to prove the living can benefit the dead (Isaal al-Thawab)?

See also (video)