I have an App created and deployed to SP online. The list that gets deployed with the app is empty and I need to migrate data into it. Is it possible to import a SharePoint list (.stp) into a SharePoint online App Web? If not, what is the recommended way to get List data to the cloud?
You can export the list to excel and then import it into SharePoint online list.
Also check this KB articles for more detailed information about how to manually migrate the content to the office 365.