No, you cannot directly move emails to the predefined categories: (Updates, Social, Forums, and Promotions) within the ‘Move to’ drop-down menu.
However, you can utilize the "Apply category" feature to categorize your emails effectively. This feature allows you to assign a category to an email, ensuring it is organized and sorted into the appropriate category. Simply select the email and use the "Apply category" option in the message action bar to categorize it accordingly.