Final answer:
In The Book Thief, the Mayor's wife does know that Liesel is stealing books. There are multiple instances in the book where the Mayor's wife hints at her knowledge of Liesel's actions. For example, she asks Liesel about stealing books and gifts her a book during the Christmas celebration.
Step-by-step explanation:
In The Book Thief, the Mayor's wife does know that Liesel is stealing books. We know this because there are multiple instances in the book where the Mayor's wife hints at her knowledge of Liesel's actions. For example, in one scene, she asks Liesel, 'Have you been stealing books again?' Additionally, during the Christmas celebration at the Mayor's house, she gifts a book to Liesel, which implies that she knows Liesel's love for books and supports her in it.