Work-around: For now, I have implemented a workaround by creating a dummy FB user for the group. I have set all group notifications on for this user, which makes sure that all posts are delivered to the gmail inbox of this user.. Next, I used a WordPress plugin called Postie to allow me to post by email. This way all posts on the group are getting blogged on my wordpress blog..
This does not give me allow me to export previously posted content, but
all new posts are being taken care of.. (You can actually export the
previous content too, if you already have notifications set for the
account that you want to use for blogging)
I know that blogging by email is a native functionality that WP provides, but Postie is much more robust and versatile. Also, I made some code level changes to add functionality like adding tags to the post depending on the content. (I asked the group members to use Twitter type hashtags that are later added as blog tags)