Facebook Group Wall Posting Through Our Website - repost 2

We are interesting in creating a website through which users of a Facebook group can post through our site to the wall of the group. For example, would the admin of the Facebook group have to install an app that you will create that will enable users of that group who are registered in our site to be able to post to the groups wall. Also admins of groups and pages can post to the walls of pages and groups they manage through scheduling them through our site. Sprout Social enables admins to post to the Facebook pages they manage only. We want something similar but we want members of a group to be able to post to the group wall. This is the core of our website. Your recommendations are welcome. What you need to tell us if this is possible and how you and what you need to build it.