Disable Outlook Auto-Mapping with Mailboxes
If you wish to give a user full access to a mailbox, but do not want to have the mailbox auto-map into the users Outlook profile, assign the full access permission with with the -AutoMapping parameter.
Add-MailboxPermission mailboxname -user username -accessrights fullaccess -AutoMapping $false
Add-MailboxPermission mailboxname -user username -accessrights fullaccess -AutoMapping $false