Zaunkoenig

With this plugin admins are able to communicate with their users. That is useful if you have a website where you don\’t want your users to talk with each other. Every term of the plugin is customizable, so you can translate it in your own language.
You will need to create some pages, to put following shortcodes in:
Inbox-Page: [admin_user_messages_inbox]
Sent-Messages-Page [admin_user_messages_sent_messages]
Write-Message-Page: [admin_user_messages_write_message]
Read-Message-Page [admin_user_read_message]
Answer-Message-Page [admin_user_answer_message]
Search-Page [admin_user_messages_search]
<h3>Update Notice</h3>
0.1.3
<h3>Update Notice</h3>
0.1.4 Secured function if another plugin uses same function, so it don’t has to be redeclared
<h3>Update Notice</h3>
0.1.5 
– bugfix mysql error when someone calls sent messages and still no message is sent. See support forum read_message.php Error 
– bugfix set dynamic term page on sent messages page. See support forum read_message.php Error
<h3>Update Notice</h3>
0.1.6 
Big update! Now it is possible to search within the messages. That is usefull if you have many messages. It is a full text search in the messages and their subjects.

Admin User Messages

Admin User Messages is a simple plugin that allows communication just between Admin and single users, but not a communication between user and user.

kingdijk

This extension allows shoppers to be able to send different types of messages to the shop owner (seller) directly from their Individual Account page. The types of messages include; product-related messages, order-related messages, refund-related messages, and dispute-related messages. The shop owners are also alerted by email on receiving new messages from shoppers.
SUPPORTED LANGUAGES
<ul>
<li>This plugin support multiple languages: ENGLISH, FRENCH, CHINESE, TURKISH</li>
</ul>
An inside look:
<iframe loading="lazy" class="youtube-player" width="750" height="422" src="https://www.youtube.com/embed/wz-0BMiffjo?version=3&rel=1&showsearch=0&showinfo=1&iv_load_policy=1&fs=1&hl=en-US&autohide=2&wmode=transparent" allowfullscreen="true" style="border:0;" sandbox="allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox"></iframe>
KEY FEATURES (CUSTOMERS)
<ul>
<li>ALLOW USERS INQUIRE: Customers can inquire on any product from the product page.</li>
<li>PRODUCT PAGE CTA: Insert and customize CTA section on products page</li>
<li>CUSTOMER INBOX SECTION: Customers get an ‘inbox’ tab on their “My Account” page, where they can use to communicate with store admin</li>
</ul>
KEY FEATURES (STORE OWNER)
<ul>
<li>TICKET BASED MESSAGE MANAGEMENT: Manage your correspondence as tickets and keep try of latest messages with ease.</li>
<li>TICKET STATUS: Moves ticket across different status and keep track of changes: OPEN|CLOSED|ARCHIVED</li>
<li>ASSIGN TO OTHERS: Easily assign messages to other team members</li>
<li>ACCESS CONTROL: Control which admin user has access to your store messages</li>
<li>SEND MESSAGES: Quick send out messages to any of your contact or new email address</li>
<li>NOTIFY CLIENTS OF NEW PRODUCTS: Got new stock? Easily notify customer who have purchased similar in the past of new store</li>
<li>AUTO-RESPOND SETUP: Setup automated store responses to messages from customers</li>
</ul>

Inbox For WooCommerce

Receive messages & inquires on products/services from customers. Start a new message or manage messages from within WordPress admin.

Admin User Messages vs Inbox For WooCommerce