The Supplication said Upon Completing the Recitation of the Quraan During Taraawih Has No Basis Whatsoever
Questioner: The supplication said upon completing the recitation of the Quraan, especially during taraawih, does it have any basis?
Al-Albaani: No, it has no basis.
Questioner: The supplication said when one finishes reciting the Quraan?
Al-Albaani: Upon completing the recitation of the Quraan … when a Muslim finishes [reciting all of it], it is a Sunnah for him to, or it is mustahab for him to supplicate and gather his family to do so.
As for when the Quraan is completed like this in the prayer, in the night prayer, then this long, extensive du’aa has no basis whatsoever.
Also see Shaikh Uthaimeen’s answer on the same topic here.