Messenger Button On My Web Page Advice

hi,
This is driving me nuts so here is my site url.
https://www.theremotedoctor.co.uk/index.html

If you look at the headers you will see one celled CONTACT.
If you click that in the sub menu you will see Messenger.
Now what i am trying to do is when a customer clicks on it there messenger will open ready to message me etc.

I can click on it & Messenger opens fine,but then its my pc,my page,my account etc so maybe it will work.
Other people tell me they click it and advised its broken.

Any advice is welcome.

This code i have in use on the mentioned button.

<li><a href="https://www.facebook.com/messages/t/ian.parsons.1840" target="_new">MESSENGER</a></li>

 

This is what I get.

 

It opened a Messenger tab for me. I'm currently in the midwestern United States and used Chrome and the new Edge browser.

 

I'm in South Africa and used Dolphin browser on an Android phone.

 

Hmmm something isnt quite right then.