All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Since this woman has observed the fast while intending supererogatory fast, so considering those days as missed days of Ramadan is incorrect since it is confirmed that ‘Umar narrated that the Prophet said: "Indeed, deeds are judged by intentions, and a person gets the reward of what he had intended.".[Al-Bukhari]
Since, she had observed optional fast, then it is not permissible to consider it as missed days of Ramadan. She must fast all the missed days of Ramadan. In addition to this, she has to feed a needy person for every day as expiation since she had delayed fasting before the next Ramadan came. However, if this delay was for a sound reason, then she has to make up the missed days only. We would like to inform this woman that whoever is able to fast has to fast and nothing can replace it.
Allah knows best.