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.
It is an obligation upon your wife to make up for the days of fast she missed last Ramadan due to her menses, as well as the days she missed this year because of breastfeeding, and she cannot resort to expiation (feeding the poor) instead of fasting.
If she had delayed making up the missed days of last year without a legitimate excuse, like being able to make up during the year until Sha’baan but she willingly did not make them up until the advent of this Ramadan, then she is obliged to make up these days as well as paying the expiation. The expiation is to give out around 750 grams of food (from what people commonly eat in the country you reside in) for every day she missed.
Allah knows best.