Praise be to Allah.
The hadeeth mentioned was narrated by al-Hakim and was quoted by al-Hafiz and al-Mundhiri in al-Targheeb wa’l-Tarheeb. He said, It was narrated only by ‘Amir ibn Khadash al-Nisapuri. He said: our shaykh, al-Hafiz Abu’l-Hasan said: he was a narrator of munkar (rejected) reports. He was the only one who narrated it from ‘Umar ibn Haroon al-Balkhi, who is matrook and mutahham (i.e., his hadeeths are rejected), and only Ibn Mahdi praised him.
Hence it is known that this hadeeth is da’eef (weak) from the point of view of its isnad (chain of narrators).
Moreover, the saheeh ahadeeth (authentic narrations) indicate that it is not allowed to recite Quran when prostrating, so the hadeeth is also weak from the point of view of its text. It is not permissible to act upon it because it is not saheeh (sound) and because it contradicts the saheeh ahadeeth.
And Allah is the Source of strength.