Can a mother through breastfeeding inherit?

Praise be to Allah.

A mother through breastfeeding is not entitled to inherit from the child whom she breastfed just because she breastfed him, whether he has heirs or not. 

She may be entitled to inherit for some other reason (other than breastfeeding), such as if she is the grandmother of the infant, or a sister through ties of blood. In that case she is entitled to inherit because of being closely related. 

And Allaah is the Source of strength.