Open messenger dialog on click of another element

I would like to know if it is possible to programmatically trigger the click of the messenger icon.

When clicking the messenger icon manually with the mouse, the dialog opens. I have a certain block on my homepage which reads “Live Chat” and when the users click there, I want the messenger dialog at the bottom right of the screen to open as it does normally when you click on the messenger icon.

I tried multiple methods to do this. Some of them were:

1.Using jquery, on clicking my live chat div element, perform a jQuery.click() on the #fb-root root element and have also tried all of the child elements one by one with no success.

2.Tried to perform a triggered click on specific coordinates at the bottom right of the client’s window, right above the messenger icon but again with no success.

Could anyone suggest a working way to programmatically perform a click on the messenger icon by clicking on other elements??

Thanks in advance, Aristotelis.

The page I need help with: [log in to see the link]