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Yes, it is available for selection and I select it and then the first picture/video is the one that becomes the cover.

Oh, got it. So the cover image is replaced by a video that is at the top of the post. Unfortunately this is not easy to fix (video are a bit different and not handled as normal pictures). I'll try to see if there is something I can change and let you know.

The video is the second picture. The black and white one is the cover now and the first post. Then the video is the next one.