Google Apps for Business users can create "Nicknames", or aliases, for their accounts. An alias is an alternative email address that points to an existing user account, and can be used for both incoming and outgoing messages. Postbox users who would like to send messages from an Google Apps nickname can use the Identities feature. Here's how:

1. Create a Nickname in Google Apps. For assistance, please follow the steps outlined in this Google Support Site: Email Aliases - Google Apps Help
2. After the nickname is created, it must be added as a sending account online. Log into Google Apps Mail and go to Mail Settings | Accounts | Send mail as, and add the alias. Use the default settings, and make sure you verify ownership of the account before continuing.
3. In Postbox for Mac, go to: Postbox | Preferences | Accounts | <your Google Apps account> | Identity, If you're using Windows, go to Tools | Options | Accounts | <your Google Apps account> | Identity. Then, click the Manage Identities button.
4. In the window that appears, click the Add button to create a new Identity. Fill in your name, your nickname as the email address and click OK. No other changes need to be made. 
5. When composing a message, this new identity will be available when choosing the From address. The recipient will see that it was sent from the alias, and not from the main account.