heiress to

"Heiress" is someone who has inherited. This usually means significant wealth, but it this case, it means significant knowledge.

Yes. Heir and heiress both are often used to denote the maintenance of a tradition or a practice. So, suppose a woman were a patroness of the arts, and collected many paintings. If, after her death, her daughter continues the practice, one might write: "Susan was the heiress to her mother's reputation as an art collector." If Susan's father was the kind of man who would grow angry with people who thwarted his will and sue them for it, and she displayed the same trait, one might write: "Susan was an heiress to her father's litigious nature."