More probable the DGI - Cubas Intel service as retaliation for the multiple attempts on Castro. The KGB was likely aware of it.
The whole lot: Romanian, Cuban, Polish, East German, etc. were subordinate to the KGB. The "peacenik/disarmament" leftist crowd in America were also subordinate to and funded by the KGB.
The Cuba theory may have some merit. Oswald belonged to the “Fair Play for Cuba Committee” after the USSR turned out not to be what he was hoping for and he had returned stateside. He attempted to visit the Cuban Embassy in Mexico City at some point.
“The KGB was likely aware of it.”
Maybe not. Our greatest spy asset of the Cold War, Morris Childs, was in Moscow, in the Kremlin, hanging out with Soviet Union’s highest officials when Kennedy was shot. They were just as shocked as we were and were running through every scenario that they could think of as to could have killed him. The Soviets had a sort of grudging admiration for Kennedy. Morris Childs story is amazing, he was the money courier for the CPUSA and the Soviets never suspected him.