How to detect Facebook in-app browser?

You can check for FBAN / FBAV in the user agent.

Check this link: Facebook user agent

You can use https://www.npmjs.com/package/detect-inapp and check if inapp.isInApp() is true

To complete worker11811's answer on using the user agent, here's a code snippet to make it work:

function isFacebookApp() {
    var ua = navigator.userAgent || navigator.vendor || window.opera;
    return (ua.indexOf("FBAN") > -1) || (ua.indexOf("FBAV") > -1);
}