Do you mean a website that supports chess diagrams (like here) or one that doesn't? If it does then you can copy the pgn file but if not you probably can't make that diagram because a pgn file alone won't do anything and can only be opened by chess programs and a "diagram creator" or whatever you want to call it, but that's the only chance you have of copying a diagram I think. I'm not 100% sure though.
Of course I have no idea how these "diagram creators" were made here but it's probably very complicated.
Do any of you know of a site where I can make interactive chess diagrams, like what are used to play through games on this site, and then link them directly to a different website?
If so I would really appreciate it. Thanks in advance.