When creating the task, there is an option for the creator to be notified when the Task is completed or overdue. If the Task isn't completed by the set due date, you will be notified.
You can also check by using the advanced search feature within Tasks. This can be accessed by clicking on the filter icon next to the search bar. Select your name in the "Assigned By" bar (either start typing or selecting it from the drop down menu), and the other person's name in the "Assigned To" bar. From here you can see all of the Uncompleted Tasks and the Completed Tasks you have assigned to them.
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