It has been reported that the Soviets were amused by the first American bomb, mocking it, since it was the size of a small house, relying on a considerable array of cryogenic devices. They obviously knew about it, but that knowledge was not critical to their success.
Sakharov also developed the Tokamak fusion reactor concept. When the temperatures reported for the reactor was announced by the Soviets, the British sent a delegation to Russia to confirm the numbers, since the Western world suspected the announcement was a propaganda type lie. The British confirmed the result.
The horror that Sakharov experienced after the Tsar Bomba nuclear test, to this day the largest nuclear weapon ever developed, caused him to become a dissident.
He was, besides his political activity, marking him as a great man especially considering what he surrendered to dissent, a truly great physicist, equal, and perhaps even better than the American physicists working on fusion systems.
It is true that Karl Fuchs, an important physicist who worked on the plutonium implosion project during the Manhattan Project, his work being critical to its success, was a communist and a Soviet spy, who aided the Soviet nuclear program, expediting it but not critical to preventing it.
Russia, Britain and France all developed nuclear weapons largely independently, although British scientists (Fuchs was a British citizen), played key roles in the Manhattan project, and didn't have far to go.
One can now learn on the internet how to make a nuclear weapons; the restriction being access to materials, not military secrets. There really aren't all that many nuclear weapons secrets, and probably never really were. Anyone with the resources to do it, could. There are many papers published in the scientific literature discussing weapons design, notably, those by Kessler et al on how to denature plutonium to make it useless for nuclear weapons.
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