When user mailbox have multi email addresses, for example firstname.lastname@example.org and email@example.com, primary email address is firstname.lastname@example.org. And he wants to send a mail with mail address from email@example.com. Then he will get a NDR that he does not have permission to send as firstname.lastname@example.org.
This is by designed. Do not try to change the behaved.
To help user get what he want, here is a workaround.
1 create a new mailbox for him.
2 assign full access and send as privilege on the new mailbox for him
3 change primary email address on the new mailbox to email@example.com at the meanwhile change his own email address to firstname.lastname@example.org
4 ask helpdesk engineer to add the new mailbox opened in his mailbox account from outlook account settings.