The "Message Us" plugin can be used to immediately start a conversation and send the person to Messenger. On the desktop web, the user is sent to messenger.com and on mobile they are sent to the Messenger native app.
<div class="fb-messengermessageus" messenger_app_id="<APP_ID>" page_id="<PAGE_ID>" color="<blue | white>" size="<standard | large | xlarge>"> </div>
For a complete description of available attributes, see the message us plugin reference.
This plugin does not trigger a callback to your webhook. However, you will receive a message callback when the user sends a message to the page.