Ṣalāt-ul-witr missing Qunūt

A person performed ṣalāt-ul-witr on their own. They forgot to recite the du’ā of qunūt in the third rak’ah and performed rukū’. They then remembered that they had missed the du’ā of qunūt, so they stood back up and recited the du’ā of qunūt. They performed rukū’ again a second time and completed ṣalāh, performing sujūd-us-sahw at the
end. Is their ṣalāh valid?

In the Name of Allah, the Most Gracious, the Most Merciful.

As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh

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