Is it possible for a foundling to become mahram without being breastfed, and how is inheritance handled in the case of possibility and impossibility, for a barren woman who is caring for a foundling less than two years old and is unable to breastfeed him for health reasons?

It is permissible to raise a foundling provided that he is not attributed to the one who found him. It is obligatory to establish mahramiyyah (unmarriageability) between the female finder and the foundling through breastfeeding before he reaches puberty, by having her or one of her female relatives breastfeed him a known number of times. There is no inheritance between the foundling and the woman who found him, even if he becomes her mahram through breastfeeding. As for the spouses, they inherit from each other according to the rulings of Islamic inheritance.