Within Teamwork Projects you can set specific permissions to allow a user to edit a file that has been uploaded by any user.
Note: By default this permission will be disabled when a person is added as a user to a project but if you upgrade them to project admin they can then edit any project file.
To enable the permission to edit files click on the 'People' section to the top of the screen:
From the list, choose the user you want to update and then select the green edit button to the top right:
You can then select the permissions tab on the pop up window that appears. To the bottom you will see what project access the user has, click on the 'edit' option:
Next to the project you want to give file editing permissions on click edit to the right:
Under the permission 'View messages and files' you can tick the 'Update Files' to allow the editing of any updated project file.
Note: If you disable this permission the user will be unable to edit existing files or upload new files to the project.
For more information see: Uploading files in the files area