Here are the steps required to allow a non-Google user access to a Google Site. 1. Open the edit page of the Google Site.  Select the Share with others button 2. Enter the email address that you want to grant access to the site 3. Finish entering the information. Be sure that permissions are set to "Published Viewer".  You can include an optional message to the recipient.  Also, be sure the "Notify people" checkbox is checked.  Click "Send" The next steps are very important to guarantee that the user can properly authenticate and access the site.   4. The invitee will receive an email with a button to open the site and go through the verification process.  They should click "Open" 5. Their web browser will open and they will see the following message.  They should click "Send" 6. They will see the following message. Once the verification code is sent to their email, they should enter it in the box and click "Next" 7. The website will open for viewing

NOTE:  If you are trying to grant a non-Google user access to a Google Site (like Place Toolkit),  please refer to this article: https://www.placehelpdesk.com/support/solutions/articles/19000031066.  

If you are a member of a Google distribution group, in addition to receiving mail sent to the group, you can also send mail from the group address. Here's how to set that up in the Google web mail client. Go to mail.google.com and login as your primary user In the upper right section, click the Settings gear and then click the See all settings button under Quick settings In the top menu bar, click Accounts Under Send mail as, click the Add another email address link You'll see a yellow popup.  Enter the distribution group address in the Email address box, leave the box next to Treat as an alias checked and click Next Step Click Send verification You will receive a verification code by email (sent to your distribution group address).  Enter that code into the box and click the Verify button You will now see your distribution group address as one of your Send mail as options When you compose an email, you will see that address as an option in the From address