Copying the hyperlink from the mail and pasting it into browser - NOT WORKING.
Received the same error. You are not authorized to respond to this task.
I know this is a much older question, and I hope that you were able to resolve this issue by now, but I wanted to share something that we did to avoid this.
We created a SharePoint User group with the users that need to be assigned to the task as well as the shared mailbox. Then, in the task, select the newly created SP user group as the assignee in the task. Be sure to keep the "Create individual tasks for all group members" unchecked so that it creates a single task that everyone can then access.
Hope this helps!