Send As From Google Group
1. Login to the business account primary email (the owner / admin).
2. From Gmail, go to Settings > Accounts and Import > Send mail as. Add the Google Group address here once.
3. Login to your personal email account in Gmail, which should also be a member of the Google Group to receive messages.
4. Go to Settings > Accounts and Import > Send mail as. Add the same Google Group address here again.