Julian Yanover

Admin Msg Board is a plugin for WordPress that will add a messaging system in your WordPress admin area. This works for weblogs that are written by more than one blogger, so they can communicate with each other, without leaving the WP system. 
Messages can have up to 140 words like in twitter, and you can choose whether to write to all users or select recipients

Admin Msg Board

Adds a messaging system in your Wordpress admin area for bloggers to communicate.

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 Msg Board vs Inbox For WooCommerce