Hi there,
I'm Alex, can handle the issue. As I imagine you take the link of the story and want to post it on your personal/business profile but it shows only the photo but not a title and thumbnail - yes?
If yes, then I could fix this. Need to make function that Facebook would take exact text/title from the story page, because I assume there are no such function. You won't make it via your CMS - I guess you use WordPress. So this could be made only through backend.
Let me know for further details.
Thanks
Alex