The Email for Trello Power-Up allows you to set up your own custom email address (e.g. firstname.lastname@example.org) for sending and receiving emails in Trello. If your company uses a Google Group you can use the group email address as the custom email in Trello. This means that rather than an actual mailbox with forwarding rules, you can use a Google Group to redirect inbound emails to your board. You can read more about custom email addresses here.
To link your Google Group email address with Email for Trello you can simply add the SendBoard board address as a member of your group. Emails sent to your Group address will then be forwarded to your board.
Add your board as a member of your Google Group
Open your Google Group, select Members from the sidebar and click Add members.
Copy the Trello Board Address into the Group members field and click "Add Members". This will add your board as a member of your Google Group. Emails sent to your group address will be added as new cards on your board.
Allow external members to be added
You will need to make sure that your Google Group access settings allow external members to be added to your group. This is necessary to add the SendBoard board address to your group.
Select Group Settings from the side panel. Scroll down to Allow external members and select 'On'.
Note that you will need to have access to Groups to manage group settings. If you cannot see that option, you may need an administrator to change this setting on admin.google.com.
Note: Inbound emails need to arrive at SendBoard using the FROM address of the original sender/author. So make sure the "Author's address" is selected as the Default Sender.