Answering mail to original poster using group address

Goal

I want to handle support email using support@example.com. The public must be able to send mail to support@example.com and receive replies from support@example.com only. Mail sent to support@example.com will be handled by a few people, including me.

What I did

• I have a G Suite basic account with complete administrator permissions. My personal email address is flux@example.com.

• I have enabled Groups for Business, and I have set up a group as a collaborative inbox with address support@example.com.

• In https://groups.google.com/a/example.com> Manage Group > Settings > Permissions > Posting Permissions, I have enabled all members of the group to "Post As The Group".

The Problem

• I have just received a new mail (i.e. a new Google Groups post) that a customer sent to support@example.com.
• In the web interface, I clicked on the reply button, bringing up something like this:

• But how can I actually reply to the mail using support@example.com? If I click on "Post" to send the reply right now, an email will be sent TO support@example.com and CCed to the customer who emailed support. I don't want this behavior because the customer will see that I sent the reply to two "people" (i.e. TO support@example.com and CC to the customer). This is what the reply will look like to the customer:

Notice the "to Support, me". I don't want that. I want it to be "to me" instead. I cannot uncheck the CC "Original author" checkbox because my customer will never receive the reply if it is unchecked.

• What I want is extremely simple:
  • Customer sends mail to support@example.com.
  • support@example.com replies to the customer's mail (using TO and not using CC).

How can I fulfill my apparently very simple needs using G Suite?

Notes:

• I have read Answering mail to original poster as group. That user did not seem to encounter the problem I explained above.