1) Open the browser, then open your email account. Click the
settings icon>
See all settings.

2) On the Settings screen, click the
Accounts and Import tab

3) Under Send mail as click add another email address.
4) See the image below:
5) Click the send Verification
6) Provide the verification code that sends to your email.
7) On your Gmail click compose>New Message>Click the dropdown arrow then select the group email you add to send outgoing messages.