You can set your Gmail account to allow you to send a message from a collaborative inbox .
If you have permission to do so, you can add a new From address to Gmail so that you can send messages from yourself or another person or Google Group when you compose a new message or reply to a message in Gmail.
To add a new From address to your Gmail account:
Click on the Settings cog in the top-right corner of the screen and choose See all settings
Click on the Accounts and Import tab
Next to Send mail as, click on the link to add another email address
Type the name and email address you wish to send mail from
Click on Next step
Click on Send verification to send a verification email to the specified email address to confirm that access should be granted
An email will be sent to the email address you entered, asking for confirmation that this address can be used.
To accept the setting, go to your Google Group and open the message confirming the new setting. Click on the link to confirm you wish to add the new From address.
When you add a new From address to Gmail, a From field will be added to each message you confirm, allowing you to choose who you wish to send the message from.
The message will be sent to the recipient from the person you choose from the From list. The other name in the From list will not appear anywhere on the email and it will not be sent “on behalf of” the new sender.