People Can Send Me E-mails, But They Can't REPLY to My E-mails

So the person I want to send these e-mails to has saved my e-mail address and Digital ID in their Outlook Address Book. This person can now SEND me e-mails, but they cannot REPLY to my e-mails. What needs to be done on their end so that they are able to REPLY to my e-mails?

Also, this is the ONLY person I want to send digitally signed/encrypted emails to. What is it that I need to do to make it so that no one else gets digitally signed e-mails from me?