If you encounter a problem sending an email from your Exchange mailbox to a specific recipient but sending emails to that recipient from other mailboxes is successful then that is most likely due to cached contact details in your mailbox. You will get a bounce-back email with an error message like this:

Delivery has failed to these recipients or groups:
[recipient]
The e-mail address you entered couldn't be found. Check the address and try resending the message. If the problem continues, please contact your helpdesk.

To resolve this problem you need to remove the cached details. To do that you can start composing a new email and type the name of the contact in the To field. Then when the auto-complete box appears, click on the X symbol and that will clear it from the cache. Further emails to that recipient will then be sent successfully. There are full details on this issue in this Microsoft knowledge base article.