I got around this with several steps. some of these may not be needed.
My example is an approver task.

1. Created a shared mailbox
2. added the shared mailbox as a participant in Nintex
3. I created a distribution group with the shared mailbox an all the members who are approvers.
4. Created a group in Nintex with all the approvers.
5. Added the approvers nintex group as a busness owner on the workflow. **(you may be able to just add the shared mailbox).
6. added the distribution group to the Task email (max 20 members for the group).
7. used an exchange transport rule to filter out all emails except to the shared mailbox. (individual mailbox rules can do the same)
8. Use can then click the link, (which for me also appears in my IT ticketing system)

The end result is the users can click the link, and when they approve , if you look at the Task Status and it will show the task assigned to the shared mailbox was Overridden by that person and completed.
The approves do not see they emails but can still approve.

The big part is the must be business owners of the workflow to override. You can try with just the shared mailbox. My use case is different, they are not in the shared mailbox. But I bet it will have to be the same unless they are actually logging into the shared mailbox with the username and password.

Hello @SShaffer2 , you need to decide if the following method will work for you:

If you disable Assignee Authentication, you can just pop the shared mailbox email address into the Assignee field. 

Hello @SShaffer2 , you need to decide if the following method will work for you:

 

If you disable Assignee Authentication, you can just pop the shared mailbox email address into the Assignee field. 

 

 

The caution with this is that anyone with the link can click it.
Also if it is important to find out who clicked the link, the “completed by” field only shows : Anonymous form submission

@Scottg - Hello, thank you for such a detailed response.  I will give some of this a try.

@Deon - Thank you for your response.  I will give this a try to see if it works.  

@Deon Hello, I disabled “Assignee Authentication”, and that gave the user the ability to open the task.  Thank you for that suggestion.  However, on the task form, I have a people picker that allows the user the ability to provide a name.  When “Assignee Authentication” toggle is disabled, the user gets “Content Failed to Load” when trying to use the people picker.  Do you have any suggestions around this problem?

Hi @SShaffer2 , unfortunately the People control is supported only on authenticated forms. 

Depending on your use case, you can potentially use a Choice Single control hooked up to a Data Source Variable which uses a Azure Active Directory Query Users Data Source. 

You might then use various filters to prevent the drop-down from containing a gazillion users for example.

@Deon

Thank you. 

When the task is sent to the Shared Mailbox, I can open the task, but others cannot.  I am a Global administrator and Site Owner.  Is it possible that my permissions make it possible for me to open and others cannot?  In O365, we got around the issue of Shared Mailboxes by giving everyone permissions to the Workflow Task list.  But, since there is no Workflow Task list in NAC, is there something else we can give everyone permissions to?

Thanks.

Hi @SShaffer2 , yes, I also fell into that trap before - as a Global Admin you can action any task so yes it is because of your permissions.

If you use authenticated task forms, then in NAC, unfortunately the task can only be opened if the task was explicitly assigned to that user.

It does not currently have the ability to check if a user is a member of a Group and allowed to open the task, if the task is assigned to a group.

@Deon - Thank you for all of your help. 

If I specify all of the names of the people who access the Shared Mailbox as the “Business Owners” of the workflow, then they should be able to open a task sent to the shared mailbox.  Is that correct?

or

If I specify “Everyone” as the Business Owner, then everyone could open the task. Is that correct?  I understand by doing this, I will not be able to use functionality designed specifically for Business Owners, but if I don’t need that functionality, I should be OK, right? 

Yip, that should work @SShaffer2 .