Translation:We have no proof that they have stolen something.
Since this is a negative sentence, a more natural translation would be, "We have no proof that they've stolen ANYTHING."
In my case ,the correct answer was - we haven't got any proof that they have stolen anything.
This is a very awkward and unnatural sentence in English. We would rather say: "we have no proof that they stole anything".
Duolingo is attempting to keep the English construction as analogous to the Russian as possible. This is for the purpose of understanding the Russian construction, even if the English is awkward
Exactly. That's why I don't report exercises like this, and instead leave a comment so that people who aren't as strong at English realize that this is not how a fluent English-speaker would construct the sentence.