The Professor Weasley’s Assignment quest in Hogwarts Legacy will be obtained after meeting Poppy during the Stop Ranrok and Rookwood main object as part of the story. Professor Weasley will task you with collecting the Field Guide Page from the Underground Harbour. To reach it, travel to the Viaduct Courtyard Floo Flame in the Grand Hall then head down the small flight of stairs. Follow the path hugging the right wall. The entrance to the Underground Harbour can be found on the right just before the end of the overhang. This will be near a werewolf statue. You can then travel to the harbour and use Revelio to locate the page.
The other task will be to collect the Field Guide Page from the Intermediate Transfiguration book in the library. Travel to the Library Floo Flame in The Library Annex, head up to the 2nd floor and make your way to the northeastern corner. Speak with Sophronia Franklin. She will give you the book only if you agree to answer questions from her quiz. It doesn’t matter if you answer the questions correctly or not as either way she puts the book back on the pedestal. You’ll also have the option to answer more of her questions. If you answer them all (either correctly or not as it does not matter), she’ll give you potions. When you’re ready, use Revelio on the book to collect the Book on Intermediate Transfiguration guide page.
With all the tasks completed, head to the Transfiguration Classroom in The Astronomy Wing during the day to attend class to learn the Transformation spell. Speak with Professor Weasley after class to complete the quest.