Sending, receiving, and organizing email in Outlook.com
Hello, good day and thanks for your question. Sorry to know about this and I understand that emails from your son were deleted.
This is unusual because even if a specific email address is already closed or not active anymore is that any email will not be or should not be deleted from an inbox or from the recipient's email.
In this scenario, you may check the deleted items or check the other folders like spam, junk and search thoroughly for it as retrieval will be difficult and impossible if there is no backup for it.
May I also check and confirm on which email provider you are using and if this gift card is from Microsoft or from another store or company?