The instructions below will show you the steps necessary for you to be able to send email out using your google groups email address. You will be adding the Group Project Google Group email address as an alternative / alias address to your individual Connect Gmail account. Any responses to the emails you send will go back to the group and be received by all members depending on how your have your Google Group setup.
Step 1) Write down your Group Project Google Group email address, you can find this in the Google Groups interface.
Step 2) Log into the Gmail account you wish to send email from, this will be one of the group members Connect Gmail account. This guide can be repeated for additional members of the group allowing multiple people to send emails using the Group Project Google Group email address.
Step 3) Under "Settings" click on the "Accounts" Tab, then click on the "Add another email address" link
Step 4) Enter a display name, the description in use by the Google Group is a good start. The email address must be the address displayed in Step 1, your Group Project Google Group email address.
Step 5) Click "Send Verification" this will send an email containing a numerical code to the the Google Group. Depending on how you have your Group Project Google Group setup, all members will receive this email. Since you are likely a member, you will receive this email also.
Step 6) Check your individual Connect Gmail account for the verification email that was sent to your Group Project Google Group, you will need the confirmation code inside to continue.
Step 7) In the verification popup window, enter the code that was emailed to the Group Project Google Group email address and click "Verify"
Step 8) Assuming this process completed without warning, the Group Project Google Group is now listed as an account associated with your individual Connect / Gmail account, and an address you can use when composing new emails.
Step 9) In your individual Connect / Gmail account when composing a new email message, you can now select your Group Project Google Group email address as a from address in the composition window.