You need to have appropriate permissions to the mailbox in order to be able to add it.
Read the Knowledge Base articles for your version of Exchange for more information: How Do I Enable Send As Or Full Access Permissions On An Exchange Account?
Note: The mailbox you are adding should not be hidden from the Global Address List (GAL).
- On the Tools menu, click Account Settings.
- Select and double-click the email account you would like to change.
- Click More Settings.
- Select the Advanced tab.
- Click Add to open another mailbox.
- In the Add Mailbox box, type the name of the mailbox owner.
- Click OK twice.