I'm not sure you can prove it yourself - as they say, these images could very easily be manipulated by someone using commonly-available software (to say nothing of someone with access to the very expensive and highly sophisticated products available to professionals and people with money to burn). A screenshot is, after all, just another image file - there's nothing special about it to even prove what machine it came from or when it was done or that you were actually at that site when the "screenshot" was taken (other than what is in the image which could, as they would contend, all be manipulated quite easily and with exceptional quality as well - especially if using state-of-the-art equipment and programs).
I do, however, believe those professional users of top-of-the-line equipment and programs would possibly be able to tell if the image was original or if it had been manipulated (at least if they scanned at a high enough resolution and went pixel-by-pixel over the ENTIRE image) - but I could be wrong about that depending on how the image was taken and at what resolution and using what file format and whether or not that format was converted and a host of other things that surpass my knowledge of what is and isn't possible with state-of-the-art equipment and programs. There would most likely be subtle changes in the individual pixels which they might possibly be able to detect and if none were detected it would likely be an original (but with enough time and the proper equipment - it may actually be possible to do it without being detected or where the chances of detection were very slim - and no doubt they would have experts say that no matter how careful you checked, it would still be possible (maybe not likely, but perhaps not beyond a "reasonable doubt" and while the judge may allow it in as evidence, it would be tough to convince a jury - after all, didn't Jurassic Park look real to you?)).
So my only suggestion to you would be to find such a professional company (a very good, reputable one that can withstand intensive scrutiny at all levels and that has a professional who can stand the same scrutiny and perhaps has served as an expert withness before) and see if you can pay them to CERTIFY that the image is original and has not been manipulated and then somehow get that certified image taken into evidence along with the certification so nobody can say a substitution was made or so that a substitution can't be made. They would have their own experts examine it as well looking for the SLIGHTEST pixel evidence which could cast doubt on the whole thing - and they'd only need to find one questionable pixel to do so (and such things may be unavoidable unless you too used high-end equipment to capture and save the image yourself - I'm not sure that ordinary software can produce images or files that can stand up to that level of scrutiny).
Then, of course, these people who certified it would almost certainly be strenuously questioned in court and would need to stick to their guns. Getting them to do this if they can and are willing (knowing the consequences of doing so - time in court, filling out forms, depositions, potential liability, the effort itself, etc.) and knowing that proving it ISN'T a fake takes MUCH longer than proving it is because you'd have to check absolutely everything in the most minute detail since evidence of the change could be located anywhere on the image or the file and you'd need to say you had checked everything at a certain level of detail and resolution (and you'd need to know the level required for proof and make sure they did at least that if not more detailed) would be mighty, mighty expensive. Certainly thousands, maybe tens of thousands, and possibly even more all things considered.
They too would have their own experts examine the file and probably find someone (an "expert witness" who would argue that it was still possible). As a juror, I would probably consider the POSSIBILITY that it had been manipulated - after all the conflicting testimony - to be "reasonable doubt" that the evidence could be considered absolute, irrefutable proof (no matter what "your" experts said because their "experts" would say the opposite and so I'd be left to decide on my own and, as I said earlier, with all the realistic CGI movies we've all seen and the evidence of subtle tampering their experts would present to refute that it could be undeniable, I'd probably be compelled to admit it was at least possible and so there would be doubt and I'd have to vote that you couldn't prove it enough for me to be completely without any doubt - and that is unfortunately what you'd need to do as far as I understand how these things work though I'm certainly no lawyer nor do I pretend to be).
That was my long way of saying that, IMHO, you could not PROVE the screenshots were genuine and unmanipulated to the extent necessary to remove absolutely every shred of doubt from every juror. What I can do with Photoshop is remarkable. What people with state-of-the-art equipment and programs can do is no doubt miraculous. I think you'll be lucky to reach the standard of proof to even allow the judge to admit the evidence - and impossible after all is said and done by both sides to convince the jurors. Maybe if the images had been taken using that high-end equipment, you might have a better chance (though in the end I suspect it would be the same outcome), but if done from your PC using the PRTSCR button and Paint or whatever you used I sincerely doubt you can prove it beyond "reasonable doubt."
But this is all my opinion. I don't know what state-of-the-art equipment can or can't do - and there's equipment in research labs that probably goes far beyond what's available even to those companies and professionals.
I hope this helps. Sorry it's so long, but I got caught up in the topic and wanted to try to explain things from my perspective (for whatever that's worth).
Good luck!
