All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
You may observe the expiatory fast that is due for breaking an oath at any time before Ramadan. Rather, you are encouraged to do this right away because this fast is obligatory for you. The fasting for oath-breaking is excluded from the general prohibition on fasting during the second half of Sha‘baan (the month before Ramadan). Also, there is no harm in delaying fasting for your oath-breaking until after Ramadan even though this is not the proper thing to do, as you may be overtaken by death while you are still liable to do those fasts.
Allaah Knows best.