Move Facebook Messenger position of the chat icon

https://wordpress.org/support/topic/move-position-of-the-chat-icon/

Try using developer tools so you can get the code you need.
Insert the code in your custom CSS.

.fb_customer_chat_bubble_animated_no_badge {
    background: none !important;
    border-radius: 50% !important;
    bottom: 50pt !important;
    display: inline !important;
    padding: 0px !important;
    position: fixed !important;
    right: 8pt !important;
    top: auto !important;
}

Play with the settings, it works for me. I just moved it a bit to the top to unhide my BACK TO TOP button, as FB chat was fully covering this button.

Hope it helps.