See also the official documentation:
Help Center > Group Owners Manual > Sending and receiving group owner email messages

In Groups.io each group has an owner email address. Each moderator has a subscription option to control receiving messages sent to the owner address.

The owner-email address is listed at the bottom of the home page for each group.

Receiving Owner Emails:

Owners can set up preferences for receiving email to this address - set it to "None" or (from) "Members only". It's recommended to select at least Members or you'll currently have no way of knowing that they've sent a message, but it will be stored under their Member listing in the Owner Emails section.

The control is at the bottom of the Subscription page in each group (of which you moderate or own).
Go to Subscription, and scroll down to see the controls for Owner Email.

Your choices -

• All Emails (Receive every message that is sent to your group)
• Members Only (Receive only messages sent by group members)
• None (Receive no messages sent to your group)

If you are using a Pending Subscription notice, you should set your Owner Email to All.

Reading owner messages:

• Emails to the Owner email address are sent to your own email account (with the email address you use for your group).
• You can track them online in your group through Admin > Activity. You can use the dropdown menu to choose "Message to +owner" notices only.
• An owner / moderator (with permission) can also see them in Admin > Members in their own account. There is a button +owner Messages.

Sending Owner Emails:

Note to Member / Member Notices

You can also send a "note to member" with just the group owner email address. Your personal login email address will not show.

• Go to Members. Select the member.
• Click on "Send Message" button (at bottom of page)
• Select "From:" address (drop down menu) either Owner or personal (this is the only address that will be used).
  • Fill in Subject
  • Compose message body
    • OR
  • Change "--Notices--" (in drop down menu) to other Member Message (e.g. "Pending Subscription" Member Notice).
• THEN choose whether to check BCC: "Me" and/or "All Moderators"
• Click "Send to Member."

NOTE: The message sent will have your group's Message Footer appended.

Rejecting posts

The owner or moderators can set up canned rejection messages, such as off-topic, doesn't meet group guidelines, etc.

• In Settings, Member Notices, click on +New Notice and choose a notice type from the dropdown menu. Activate the notice.
• If you want to have more than one, edit the subject line to indicate the rejection reason.
  (Note: you can only activate one, which is the one that will be used if a message is rejected via email, but all will be available for use when you use it online.)
• When you get a post that you want to reject for a reason other than the active one, click through to the message on the website so you can select a message.
• Click on Reject and then use the dropdown message to choose a message.
• You can also tweak or personalize it here if you want.
• Click to BCC yourself or all moderators. (All mods is useful so that others know what's happening.)
• Send by clicking Reject Message.

See also: Member Notices