No, Britain did not "donate" the Nene to the Russians. I don't know where you got that, but there are a lot of schmucks out there promoting "alternative facts" about many things, and they are the likely source. I write about this in my coming book "Holding The Line: Naval Aviation in the Korean War."
The Labour government approved a Russian trade delegation in 1946 to review many items. No one in England recognized Artem Mikoyan or V.I. Klimov - (Mikoyan of MiG and Klimov of engines) - as being the main members of the delegation. who were amazed to see the Nene. Sir Stafford Crips, then Minister of Commerce, was happy to negotiate the sale of 16 Nenes and a license to produce them in the Soviet Union - on the condition that they be used for"commercial projects only." Ernest Bevan, who knew first-hand from the trade union struggle how much one could trust a communist promise, and was Foreign Minister, argued strongly against the agreement but was overruled by Prime Minister Clement Attlee (of whom Churchill had once said "A modest little man, with much to be modest about.") Admittedly, 1946 was a time when one could still cite the USSR as a prime ally in World War 2 and before the Iron Curtain had rung down "From Stettin in the Baltic to Trieste in the Adriatic..." Churchill did in the speech from which that quote comes.
When told that the sale had gone through, Stalin said "Why are they so stupid as to sell this to us?"
In the end, Rolls-Royce never got a dime in royalties, since the Russians claimed that their Nene, the VK-1, was so different in the redesign to productionize the engine (See my other post for Colonel Ross Mickey's comment about the original Rolls-Royce engine) that it was a "different engine altogether" (this was actually settled in Russia's favor in the international court).
The VK-1 was very close to the J-42 (both being efforts to "productionize" the R-R original). It's very interesting that one powered the airplane that changed the Korean air war (the MiG-15) and the other powered the only 1st-generation jet that could "hang in there" against the MiG-15.