It is not usually the author who has the responsibility to move the review from INSPECTION to COMPLETED. It is usually the reviewers with that responsibility. When you hover over the "Send to Completed" button for each of the author and reviewers, what does the tooltip say?
If you are in the INSPECTION phase are there are open defects, the button will say "Send to Rework". If there are no open defects, it will say "Send to Completed". Once all participants (*who are required to*) click on "Send to Completed", the review is done.
See the documentation about the workflow in the review:
https://support.smartbear.com/collaborator/docs/working-with/concepts/phases.html
