Praise be to Allah.
I put this question to our shaykh, ‘Abd ar-Rahmaan al-Barraak (may Allah preserve him), and he said: He can fast the month of Dhu’l-Hijjah and break the fast on the day of Eid and the three days of at-tashreeq (the 11th, 12th and 13th of Dhu’l-Hijjah), then make up those four days after Dhu’l-Hijjah, in Muharram, to make up for the days when he did not fast. End quote.
But when you fast on the ninth day of Dhu’l-Hijjah, the day of ‘Arafat, you should intend the fast to be in fulfilment of the vow, and there is the hope that you will attain both rewards together.
See also the answer to question no. 128256
And Allah knows best.