What is required to be done to atone for my mother, who did not fast Ramadan 45 years ago due to pregnancy, knowing that she is committed to fasting and prayer and was prevented by the doctor from fasting for health reasons?

It is not permissible to delay making up missed fasts until after the following Ramadan unless there is an excuse, such as forgetfulness. So, whoever forgets to make up the fasts until the next Ramadan begins is not sinful and is not required to pay expiation (fidyah). However, paying expiation is more cautious, to avoid disagreement among scholars. As for a remembered obligatory fast, it must be made up promptly, unless there is an incurable illness, in which case making up the fast is waived and expiation becomes obligatory.