Please clear away this doubt for me since I am not sure if any of this is backed by authentic hadeeth or not.
Praise be to Allah
There is no shar‘i (religious) basis for this idea, and there is nothing in the Sunnah (teachings) of the Prophet (peace and blessings of Allah be upon him) to suggest this.
Al-Sakhkhawi (may Allah have mercy on him) said: Reciting the Surah “Inna anzalnahu” [i.e., Surah al-Qadr] after finishing wudoo is something for which there is no basis and this is not the Sunnah. End quote.
Al-‘Amiri al-Ghazzi (may Allah have mercy on him) said:
Reciting Surah al-Qadr after finishing wudoo is something for which there is no basis.
Al-Jadd al-Hatheeth fi Bayan ma laysa bi Hadeeth (p.234).
Al-Albani (may Allah have mercy on him) mentioned in al-Da‘eefah (1449) a hadeeth (narration) about this and he said concerning it: It is fabricated (mawdoo‘).
There are proven du‘as and athkar (words of remembrance) in the Prophet’s (peace and blessings of Allah be upon him) Sunnah which may be recited straight after doing wudoo. The Muslim should be keen to recite them and not add anything to them.
For more information please see the answer to question no. 45730.
And Allah knows best.