@jboots77 

Do not include your mailbox recipients in the security groups, add them as a separate  task assignees in the task configuration.   Then on the task notification configuration, select each of your security groups from the Edit settings for drop down list, and set the Delivery type to None for each of them.  The email notifications will only go to the group mailboxes, but the tasks will be assigned to each of the groups.

I just want to clarify because I thought I just had it working but still received the "You are not authorized to review this item." message.

"Do not include your mailbox recipients in the security groups, add them as a separate  task assignees in the task configuration."   - By mailbox recipients do you mean the people that have access to the shared mailboxes? or the Shared Mailboxes themselves?

"Then on the task notification configuration, select each of your security groups from the Edit settings for drop down list, and set the Delivery type to None for each of them." - Done, No issue

"The email notifications will only go to the group mailboxes, but the tasks will be assigned to each of the groups." - I didn't receive an email in my personal mailbox but did get one in my shared mailbox. (that's perfect) The issue is I still wasn't able to answer on the form when I clicked on the link from the shared mailbox.

To your first question, I meant the actual shared mailboxes, not the users with access to the mailboxes.

I believe the reason you get the error message is because you are attempting to complete a task assigned to the Shared mailbox.  You are going to have to create a separate URL for the task link.  Since you don't know who is going to respond to the email, give them a link to either my tasks or my group tasks view, and require them to select the task from the list.  The OOB task link is always going to be for the task created for the particular email recipient.

Yes exactly, When the task is sent to my shared mailbox it expects the shared mailbox to answer, not whoever has access to the shared mailbox.

How would I go about creating a separate URL for the task link that gives me the access that I need? Will the task list not still have an Assigned To field that unless your in that field it will give you the "your not authorized" message?

The task link that is created by default on flexi-task notification includes the ID of the task assigned to the email recipient.  Since you don't know who will respond to the task, there is no way to include the ID of the specific task assigned to the random respondent.  The only option is to send them to a view of the task list filtered for their user, where they can select the appropriate task for completion.  Replace the OOB task link with a My Tasks view URL, (if you have checked the create individual tasks for all group members task configuration box). 

Or the My Group Tasks view, if you have not checked the box.

Create a string variable for the URL and use the variable in the address field for your insert link configuration.  You will need to change the wording to explain that they need to select the correct task.  I always filter the My tasks view to display only active tasks, and I add the related content link to the view, so that they can select the correct task, based on the related item.

I'm using 28 shared mailboxes which would mean 28 SharePoint User Groups as well. 

So my Request review "Reviewers" column will have 28 shared mailboxes and 28 security groups(approximately 5 users per group). 

The Review would go to the shared mailboxes. Those shared mailboxes would receive an email with a URL to the site's "Workflow Tasks" list. 

Depending on what user from the Shared Mailboxes clicks on the link in the email it will change the "Workflow Tasks list" to filter for tasks directed to them or their group?

Then they would just have to click on the task that was actually assigned to them and do their review? 

If the Request Review was sent to 10 Shared mailboxes, that would be 50 (5 users per shared mailbox) different tasks would be created. Only one person from each of the shared mailboxes needs to review the task. 

What would happen to those other 45 tasks that were created? Would the Request Review be stuck and unable to move forward until they answered? 

@jboots77 

In response to:

Depending on what user from the Shared Mailboxes clicks on the link in the email it will change the "Workflow Tasks list" to filter for tasks directed to them or their group? 

Every task list has a My Tasks view and a By My Group view by default.  The My Tasks view is filtered by assignee =[Me], and the By My Groups view has embedded logic that checks the assigned group for logged in user.  So, yes, SharePoint recognizes who the logged in user is and filters the list on assignee for that user.

In response to:

What would happen to those other 45 tasks that were created? Would the Request Review be stuck and unable to move forward until they answered?

This depends on how you design your task.  If you are using a flexi-task, (I rarely use any other kind), you have several approval options.  If you choose First response applies, then the workflow engine will automatically mark the tasks assigned to the other 45 users Not required, and send them a "Response no longer required" email.  The workflow will continue on without issue.