The Russians managed to steal designs from both America and Britain, otherwise they couldn't have done it so quickly.
That is not proven. They had their own project as well. Fission Nukes are not that difficult to build. They had a reactor running only a couple of years after the Oak Ridge one and the cooling solutions, control, etc on their first reactors used to get the Pu-239 for their first nuclear test are different from the Oak Ridge. If they stole that the question is from whom.
The bomb itself after that is a mostly chemistry + high precision high explosives engineering job. While a lot of it is classified till this day, when you have had a couple of accidents with Plutonium on the way you know what to aim for. They had the accidents by the way - they are documented.
Where theft happened was mostly likely later - at the thermonuclear stage.
We still do not know if it happened or not because the full Teller-Ulam and the full Saharov 3rd idea designs are classified till this day. However, Saharov originally managed only a very dirty fission amplifier a design similar to what is likely to be in use by the Norks. He suddenly went from there to 3rd idea which is practically identical to the USA thermonuclear bombs in being as clean as a nuke can get - with minimal fallout. Similarly, USA could barely muster something which needed a ship to carry for their early tests while the Russians went straight for a fusion bomb which can be delivered by aircraft. USA caught up shortly thereafter. Shall we say the stole it too?
One thing we also know for sure about that period is that 3 letters on both sides were working their asses off to get info. It takes time to get meatware assets in place to steal stuff like this. The timing of the first USSR nukes is nearly impossible for "stolen" design. Now, the thermonuclear race was different as both sides had spies deep in the enemy camp.
IMHO as some people have noted, a person "skilled in the art" can quickly figure out how it works if he has seen a working implementation. Once a secret superweapon is shown to the world, it is only a matter of time for a determined opponent with a deep wallet and access to resources and brains to replicate it. If an opponent has an above critical mass level of engineering count it done. So sure, a banana republic cannot replicate a western superweapon. Russia - any day. Just a matter of time. Similarly, China is now in the any day league. Even Iran is in that league - they have more than enough money and engineering graduates.