In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
The fast of a person who did not make up the missed fast days of the previous Ramadan will be accepted.
Answering your question, Dar Al-Ifta Al-Misriyyah, states:
Yes, it is accepted, by the will of God. However, after the current Ramadan, it is necessary to make up any delayed missed fast days of the previous Ramadan, and feed a poor person for every fast day one has delayed to make up without an excuse. When there is an excuse, it suffices to make up the missed fast days.
Almighty Allah knows best.