Thanks for the link JD.
If any of your friends with this problem are a little bit techy minded, they could try this on any one of their friends page that has no 'send message' button.
Open up the browser developer tools, F12 usually works for that, or just right click somewhere on the page and click on Inspect.
In the developer tools window, click on the Console tab. At the prompt in the console window, type or copy/paste this in...
...then hit enter. If that makes the 'send message' button appear, give it a click to see if it works.
You can close the developer tools, F12 again should do that, or click the 'X' on the dev tools window.
I'll do a video if that would be easier to follow, but it would use Chrome or Edge for the demo.