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.
You must make up for the days of fasting that you missed last Ramadan during the remaining days of Sha‘baan, (i.e., before the advent of the next Ramadan). In such a case, you are not required to offer an expiation, as ‘Aa’ishah sometimes made up for the missed days of Ramadan during Sha‘baan. She said in a Hadeeth that was narrated on the authority of Abu Salamah “Sometimes I could not make up for the days of fasting that I missed in Ramadan except in the month of Sha‘baan.” Yahya, a sub-narrator of this Hadeeth, said, “She would be busy serving the Prophet .” [Al-Bukhari]
The Hadeeth which forbids fasting during the second half of Sha‘baan, if considered authentic, does not apply to making up for the missed days of Ramadan.
Allaah Knows best.