[Ruling on a woman who prayed Fajr as four rakʿahs out of ignorance]

Answer (and Allah grants success): What appears to me is that she is not required to make up the prayers mentioned in the question, for several reasons:
1. It is related from the Prophet—may Allah bless him and his family and grant them peace—that Allah does not punish for an inadvertent increase. The Prophet (may Allah bless him and his family and grant them peace) once prayed one of the four-rakʿah prayers as five by forgetfulness, then performed sujūd as-sahw. This woman added in the prayer by mistake, and mistake is akin to forgetfulness; their ruling is one.
2. In the ḥadīth: the Prophet—may Allah bless him and his family and grant them peace—saw ʿAmmār wallowing in dust as a donkey wallows (in tayammum). The Prophet (may Allah bless him and his family and grant them peace) said to ʿAmmār: “It would have sufficed you …” etc., and he did not command him to make up what he had prayed with that (excessive) wallowing. Had making up been obligatory, the Prophet—may Allah bless him and his family and grant them peace—would have commanded him to make up the past prayers he had performed in that manner—if any.
3. The Prophet—may Allah bless him and his family and grant them peace—did not command those who had prayed in a direction other than the qiblah after doing their due diligence to repeat the prayer.
4. Uṣūl principles support what we have said: (a) Obligating the heedless is repugnant; (b) Obligating with what is unknown is repugnant. This woman was heedless of the fact that Fajr is two rakʿahs and unaware of it, believing she was correct and that Fajr is four. Had she had any doubt of her error, she would have hastened to ask.
Accordingly, she is not taken to account for the past mistake, and making up those prayers is not obligatory, due to her heedlessness of that and ignorance of it. Allah, Exalted, has said: “Allah does not burden a soul beyond its capacity.” [Al-Baqarah:286]; “So fear Allah as much as you are able.” [At-Taghābun:16]; and “There is no blame upon you for what you err in, but [only] for what your hearts intended.” [Al-Aḥzāb:5]
If it is said: Ignorance is no excuse—
We reply: Ignorance is of two types:
1. A type for which the morally responsible person is not excused: namely, he is ignorant of the description of what he has been charged with, knows that he is ignorant of it, and knows he is charged with that matter.
2. A type for which he is excused: namely, he is ignorant of the description of what he has been charged with, and does not know that he is ignorant—as in the case of the woman in the question. She believed she was correct in her act and not ignorant of the description of the prayer. This ignorance is not deliberate, unlike the first type, which is deliberate.
This may be supported by His saying: “There is no blame upon you for what you err in, but [only] for what your hearts intended.” [Al-Aḥzāb:5]
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1