Expert Facebook App Developer - Share your Portfolio of Facebook Apps

Before you apply, if you aren't an actual Facebook App EXPERT, stop. Hit back. Move along. I'm looking for help from someone who is an actual expert in deploying apps in the Facebook environment to help us understand how to get our app working in the way we need. Here's what's going on: 1. We have a software with about 1,000 users 2. Some of those users administrate a Facebook Group 3. We developed a Facebook App that's designed to post a message to a Facebook Group on our user's behalf, ideally using their name as the creator of the post. Here's an example of one such post that was automatically posted into a Facebook Group by our user "Marisa Murgatroyd" - [login to view URL] 4. The app was approved by Facebook and appears in the public app directory. And the app is connected with a verified business: [login to view URL] Now the problem .... 5. The app posts successfully using our names as long as the user of the app is an Admin for the app, and has generated a USER TOKEN, and uses that Token with the API call. However, we cannot set up all our users as Administrators obviously. 6. We tried to generate an APP TOKEN instead of a USER TOKEN to allow the app to post in its own name (which is "XP"), but we're unable to generate an APP TOKEN for it. Here's a video of me attempting to do that - [login to view URL] - it just keeps flipping back to USER TOKEN Our questions are: - Why can't we generate an APP TOKEN for this app, to allow it to post on our users' behalf? - Is there any other way to allow the App to post as the user? - What else are we missing here?