When you add a link to your Facebook page, after some processing, Facebook presents you a next/prev button to choose an image linked to the url your are inserting.
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I am not familiar with the way Facebook did it, but I can tell you how I would do it.
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This looks like a duplicate of: Facebook Post Link Image
Use <link rel="image_src" href="abs_url_of_your_image">
My guess, is that FB hides repeated images - 'couse a repeated image normally indicates a design-element (not content). When you post a link, only images related to that articles content, are relevant.
So; make sure your image only appears once, and see if it helps!