Hi,
To narrow down the issue, please answer the following questions:
1.Are there any errors when opening the shared calendar via Owa?
2. Is there hybrid deployment in your environment? Are there any users hosted on cloud?
In this case,it is a known issue for them.
Here is official doc for your reference: Outlook prompts for credentials for on premise users with Office 365 client
And here are some suggestions:
1.Please try assigning full access permission of person A’s mailbox to person B via EAC or EMS instead of sharing calendar via Outlook, see if there will be the same problem.
2.If possible, please try with other version of Outlook, such as Outlook 2019 to see if the problem persists.