Breastfeeding. Is her egg in a fertilization period at any time?

Usually not. Breast feeding produces hormone dysfunction so that fertilization usually does not occur. However there are instances where this has happened and so the necessary precautions should be observed.
Can be. There are many women who have had an unexpected pregnancy when they relied on breastfeeding as birth control. While some women do not ovulate as often while breastfeeding, they can, and you won't know you did until you end up pregnant. Without menses to predict your fertile window, assume it could be anytime and plan ahead. (BC)