Could you please help?
I have bought this video: https://stock.adobe.com/ru/video/big-raven-screaming-in-wood-wild-bird-sitting-on-branch-of-pine-tre...
Then I have used it in my music video.
Then I have received the letter from the author of this stock video with raven about that video was stolen and Adobe Stock sells it without any permission. And the author is angry and is planning to punish me.
How to solve this problem?
He can't punish you, he needs to file a copyright claim with the courts. His best option will be to rule this out with Adobe, except if you are a multimillion business with plenty of cash. Any claim he has needs to be proven.
First: When you have acquired the video on Adobe stock, you have done what you can do to protect you. Inform Adobe (link below). Give them all the data you got from the plaintiff. Ask them to assist you in your further steps.
Second: there is a possibility that someone is sending out letters without having the authority to do that. Be careful, it could be a scammer who simply wants to get money from you. If he contacted you by e-mail, check his address and credentials. If he sent you a letter check his address and credentials.
If you are persuaded that the sender is genuine, send him proof of your purchase (but edit out sensible data like your credit card number). Ask him especially to contact Adobe on this topic. https://helpx.adobe.com/stock/contributor/help/content-usage.html#Howtoreportsuspectedmisuseofyourin...
If the one sending you a letter is the owner of the artwork, than he needs to prove it and he also needs to contact Adobe and prove his case.
In the meantime look for replacement videos of a different author. If the claim is correct and the author does not get satisfaction from Adobe, ask Adobe for a replacement license and exchange the clip.
So there are 3 actions you need to do: Check if his claim is genuine, inform Adobe immediately with all the data you have at your hands, deny wrongdoing and check for replacement. If it gets serious ask a lawyer specialized in IP rights what to do.