Stupid/simple Wordpress -->Facebook -- why can't I find it?

Look for the simplest integration between Wordpress and Facebook - ever…yet I can’t find a plugin that pulls it off - to save my life.

All I need is when a post occurs on a Wordpress blog, it automatically gets added to the group wall of a Facebook Group that I’m an admin for. See?! Wasn’t that easy?

All the plugins I can find go the other way - they want to take Facebook posts and turn them into WordPress posts. I want the opposite of that. The “autoposter” plugins which seem like they might do this require setting up schedulers. I just want it to happen automatically - at the moment the post is published. Anyone seen such a creature?