How can my sister adopt a child and become his guardian such that he becomes a mahram to her and her daughters, even though she did not breastfeed him?

The forbidden adoption is to attribute one's lineage to another, while sponsoring an orphan or a poor person is one of the most excellent good deeds. The sponsor of an orphan will be as close to the Prophet in Paradise as two fingers. Due to the virtue of sponsoring those in need, the sponsor of a child who takes care of their religious and worldly affairs is considered to be in the same position as the sponsor of an orphan.

To make the adopted child a mahram to the woman who adopted him and to her daughters when they grow up, he can be breastfed by her husband's wife (if she is lactating). In this case, he becomes her son through suckling and a mahram to her daughters because he is their brother through suckling. Alternatively, he can be breastfed by her sister or her brother's wife to become a mahram to her, but he will not be a mahram to her daughters unless they also suckle with him.

If he is breastfed within the first two years with a valid amount of suckling, he becomes a mahram to her, or to her daughters, or to all of them. Otherwise, he is a stranger, and it is not permissible for him to be in seclusion with her or her daughters, and they must observe hijab in front of him.