What do you think it could be?

Thank you for your opinion, especially since it's very detailed. Now, a couple of comments:

I don't understand why the author of the topic didn't send it to the judges and/or reputable players in private first.

A judge (or rather, one judge vbn) was notified almost immediately, but at that time, the information was at the level of "thinking out loud"... and as I personally studied this situation, and with the addition of new facts, it was decided to open this topic – but only after a complete investigation.

Why weren't the results of this inquiry, even if negative, provided?

Even though I'm not a newbie in Heroes 3, I turned to the opinions of experts, both local and from other sources, but most of the answers were received before the creation of this topic and in private, and I didn't ask them to duplicate them in the topic, as I initially intended an independent examination... that is... I tried not to name the nicknames of the duel participants, and the question in private also implied an answer intended for private communication... And only once, after this topic was created, I turned to one very knowledgeable specialist – and then asked for permission to use his answer as open information – to which I received a tactful refusal...
So, I don't think that the absence of "private" results is surprising... because there are many reasons why many didn't do it, and publishing it on my part would simply be incorrect in relation to them.
By the way, all the answers in private were either 100% positive or close to it.

If there is no concrete evidence and a competent and unambiguous opinion from the judges, the accuser risks being in an awkward position and then will have to disavow his statements in every possible way. Like, I just brought it up for discussion, but so-and-so is a cheater, right?

For me, the evidence is already 100% (the only thing is that I wasn't personally present during these misdeeds – and only that is conclusive).

Let the judges decide – the presumption of innocence has not been canceled.

The judge, again, seems to be only one, and I don't want to put everything on him. I try to comment on everything myself, but I don't deny that it would be more appropriate from the judge's side.

Added after 8 minutes

The bad thing is that the saves were watched by a really excellent player; you can see this in the smallest details of the game. His talent is being ruined; on our forum, he would have become the best anyway.

Well, maybe that's it – but it seems to me that with the use of dirty tricks, any player can be strong or talented – who has played Heroes even a couple of times, and even doesn't necessarily have to know the theory well – which this opponent told me openly... it's enough to read one report every night before going to bed ;)
By the way, the same applies to offline – only there it is immediately obvious.

Added after 9 minutes

I feel sorry for online players once again. Okay, I suspected Alex_R, but how do you catch others and what do you accuse them of?!

Well, I think this will at least discourage others from cheating so openly – and maybe they will have to learn to cheat "smartly" – but for this, you need to be able to play Heroes. :)

For me, online is a game of "who can cheat the opponent more skillfully." Moreover, all this dirty business can be done on one computer and without the help of a friend... It's all sad.

I sometimes feel sad to realize this, but besides my favorite Heroes 1, 2, 3, there is also Heroes 5, in which nothing like this even comes close to happening, because there are no cheats or "peeking," and even it seems that you can't view a saved game.