Preferably also allow moving to a list that isn't mine but is shared with me in the To-Do app.
I upvoted for the idea as in the title. Although the text is also about moving it to someone elses list shared with you. Still great idea.
I am currently using a workaround to re-create the tasks that I want to move and then complete the original tasks.
However some content is lost such as deep links to one-notes where the task origined from. The link is part of the main body and can be text or HTML, but certain chars break the URL so the link is no longer complete.