Trigger Facebook Messenger with a custom website button

How do you trigger Facebook messenger using a custom button rather than the standard bottom right corner widget generated by meta supplied code? Any ideas?

Is the page live so we can take a look?

Sorry for delay - didn’t get a notification. It is live now and I found a way to do it simply my adding the following link:

It’s not what I was looking for - which was to open a chat window in the same way the Messenger widget from Meta opens - but it works ok and is decent on mobile - so is OK at least for now.