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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If this woman is able to fast, then she must immediately start observing the fast of the six days that she missed last Ramadan before this coming Ramadan starts. She may keep taking insulin injections while she is fasting unless she has to drink water after each injection, in which case her fasting will be invalid. In contrast, if she is unable to fast because of pregnancy or because her condition may get worse, then she may make up for the missed days after Ramadan. In that case she is only required to make up for the missed days.
If she is able to fast the missed days now but she does not do so until Ramadan starts, then she will be required to make up for the six days after Ramadan; in addition, she will then be required to feed a poor person for each missed day, which makes the total of six poor people. A poor person is offered about 750 gm of a food that is commonly consumed in one's country.
Allaah Knows best.