Is it permissible for a woman to postpone making up 22 days of her accumulated Ramadan fasts (70 days in total) until after the next Ramadan, due to being a university student and in an examination period, and is expiation (kaffarah) obligatory upon her for the days she did not make up before committing to it or for postponing them now, taking into consideration her financial and family circumstances?

It is obligatory to hasten to make up for missed fasts. No expiation (fidya) is due from one who was ignorant of the impermissibility of delaying the make-up until after the following Ramadan (definition). As for one who knew of the obligation to make up the fast before the following Ramadan but was ignorant of the obligation of expiation, ignorance of the penalty is not an excuse, and expiation is binding upon him, which is feeding one poor person for each day. If he delays the fast while being able to make it up, then in addition to making up the fast, he must pay the expiation of feeding one poor person for each day. This is obligatory upon him, not upon his family.