When a SharePoint task list is visible in Project Web App, but not editable, it is still possible to edit a task list in Microsoft Project Professional. If you want to edit a task list in Project Professional, there are two options:
From within Project Web App, click once in the left column for the project row to select the row, and then, on the Projects tab, in the Project group, click Open, and then click In Microsoft Project for Editing.
From within the task list in SharePoint Foundation, on the List tab, in the Connect & Export group, click Open with Project or Open Schedule depending on your version of SharePoint Foundation.
When you make changes to a task list by using Project Professional, those changes are saved to an MPP file on the site that contains the task list. If you decide to use Project Web App to edit your task list, and follow the steps in Change a SharePoint task list into an enterprise project, you also have to follow additional steps to ensure that the edits you’ve made within the MPP file are appropriately transferred to Project Web App.