Is it permissible to change one's intention during prayer from a fard (obligatory) to a sunnah (recommended) prayer, or vice versa, after having begun it? And what is the ruling if it was not specified whether it was a sunnah or fard prayer, and it was treated as one of them?

If a worshiper doubts whether he intended to pray an obligatory (fard) or supererogatory (nafila) prayer, he should consider it a supererogatory prayer. However, if he remembers that he intended it as an obligatory prayer before commencing any actions of the prayer, then in this case, he should complete it as an obligatory prayer.