This can be done using Gmail’s ‘Send email from different address’ feature.
Here are the instructions to set it up:
1. Sign in to your Google Apps email.
2. Click the in the upper-right and select Settings along the top of any page, and select the Accounts tab.
3. Under Send mail as, click Add another email address. This email address can be a Gmail account, or a group in your Google Apps account.
4. In the Email address field, enter the sender name that you want email recipients to see, and the shared mailbox email address.
5. Click Next Step >> and then click Send Verification. Gmail will send a verification message to your other email address to confirm that you own it.
6. Locate the message from Gmail. Open it and and either click the link contained in the message or enter the confirmation code in the Accounts section of your Google Apps email settings.
7. Additionally, you can also set up your Gmail to send emails from the same account in which they were received. To do this, go to the Accounts tab in your gmail, and switch on the option to do this.
Once this is set up, while composing an email, click on the dropdown next to “From” to select which email id you want to send email from: