Looking for a system to manage incoming mail from customers

I receive customer service from my clients by email. I’m looking for a plug-in (even a fee) that will import the emails directly to Woocommerce, which I can reply to directly from the Woocommerce.
That customers will be able to respond to the email and it will reach me directly without using Gmail.
I’m not looking for a customer service ticket management plugin. It is important to me that the customer send an email and not send the message from the website
Anyone have an idea? Thanks