Mrs. Morningstar says that William works at the grocery store. This is the answer given in the most direct source about where Mrs. Morningstar said William works, listing the grocery store, the post office, and the white house as options and confirming "the grocery store" as the correct one.
Another source indicates a dialogue where Mrs. Morningstar says William works at a school called the Martin Alexander Clark School of the Arts, which she refers to as the "white house," but this is about William working at the school, not literal White House. However, among the options given in the question, Mrs. Morningstar identifies the grocery store as where William works.