[Holding the Muṣḥaf and Reading from It During Prayer]

Answer (and with Allah is success and right guidance): The closer view—regarding an obligatory prayer—is that this is not permissible. Carrying the muṣḥaf in the hand is an act not from the acts of prayer, and every act that is not of the prayer is not permissible, as indicated by the ḥadīth: “Its sanctifying opening is the takbīr, and its concluding release is the taslīm.”
If, however, the muṣḥaf is not in the worshiper’s hand but is open in front of him, then there is no harm in his reading from it while praying, because in that case reading does not require any (additional) action.
Yes: it may be said that supererogatory prayers are eased, as it has been reported that they may be performed on a mount, in whatever direction it turns—even other than the qiblah, and sitting even without necessity.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1