Due to limitations imposed by Facebook around embedding you will need to use the full embed code if you wish to embed a Facebook or Instagram Post into your story.
Sadly just pasting the URL will not work for these cases.
Step 1: Get the embed code of your post.
Step 2: Paste into Exposure
Start a new Embed group type and select the "Embed your own code" tab. Paste the code from either Facebook or Instagram and click "Embed Content"
