Is there an existing possibility to trigger the share functionality in local browsers on smartphones via HTML or JavaScript?
Of course there are many services which
You could use the WebView.addJavascriptInterface() method for android.
First you will need to write a class which fires the intent to open the share menu(take a look here) and then implement that class using the addJavascriptInterface() call. After that all you need to do is call the method from your Javascript.