Process managers have an option "Complete task on behalf of assignee".
For example: you know that your team member has done the task but has no access right now to complete it. To keep the process updated, you can use this option and complete the task on behalf of this team member.
This option is available on task details page. The green button "Complete" has an extra section with a down arrow. Press the arrow and choose option "Complete on behalf of assignee"