There is a way to do this without a MOD at all. You may want to look at TwitterFeed.
I have an account with them for my forums. I simply gave TwitterFeed my forums RSS feed. Since the RSS feed is updated whenever there is a new post, TwitterFeed when it checks my RSS feed, sees new posts and then posts to the Facebook and Twitter accounts that I linked to it when I set up my account. You can set TwitterFeed to check at routine intervals (the minimum time is 30 mins I think). That's more than enough time for my forums.
Not instantaneous, but if you want to do this without a MOD it's an easy way to do it. Additionally, because Twitterfeed is a service it will automatically shorten the URLs for the links to the posts on FB and Twitter.