You might want to check out the responses in this question- Did the Stasi files prove that the USSR sponsored terrorist organizations around the globe? with answers from /u/commiespaceinvader , /u/lazespud2 , and a modest contribution by myself.

The long and the short of it was that while Eastern bloc intelligence agencies saw left-wing terrorism as a potential asset and provided some material support, the Warsaw Pact states were not really backers of these groups. Their recruitment to the ranks came within existing social networks within these Western countries and the targets of these terrorist networks had more to do with the domestic left-wing politics than with the Warsaw Pact's understanding of the geopolitical balance of power. These groups were useful, but not really trusted by the intelligence agencies.

As for the cooperation, there was relatively little in the way of joint operations. One of the facets of modern terrorist groups is that there is often intense inter-group competition and rivalries even among groups that claim to fight for the same cause. For example, both the Revolutionäre Zellen (Revolutionary Cells/RZ) and 2 June Movement (J2M) both at various points denounced the RAF as too elitist and petty-bourgeois. What was much more common was than joint operations was for individuals from one organization to filter into another either for a long period or a brief operation. Some terrorist leaders like Ilich Ramírez Sánchez (aka Carlos the Jackal) recruited among these loose networks for lieutenants, while others sought these leaders out. In the latter case, Magdalena Kopp typified this free-floating exchange of personnel; she was a member of RZ who met Sánchez via the RZ founder Johannes Weinrich and became a long-time lover to Sánchez and a member of his team.

Another form of cooperation was rhetorical in that these groups self-identified with other groups. The name Rote Armee Fraktion itself signified its self-identification with the Japanese Red Army. The Japanese group had made a major splash with various terrorist attacks such as the hijacking Japan Airlines Flight 351. Self-naming allowed these groups to control the media narrative of who they were and what they were fighting for; J2M took its name from violent West Berlin street protests against the Shah of Iran which claimed the life of the student protestor Benno Ohnesorg. The RAF moniker not only suggested a global dimension to the West German group, but also pushed back against the FRG media's description of them as the "Baader-Meinhof Gang," which suggested criminality instead of a more ideologically-motivated rationale for their activities. The Arab-Israeli conflict in the 1970s proved to be a common ideological mortar for this self-identification as these groups styled themselves as urban guerillas who were fighting imperialism in Western Europe much as groups like the PLF were in Lebanon. The first-generation of the RAF did receive training in Jordan, and the somewhat pampered West Germans made complete asses of themselves to their hosts (one of their supposed demands was for the training camp to install a Coke machine!).

The importance of the Arab-Israeli cause to the Western European left-wing terrorists does overshadow other linkages, both concrete and self-proclaimed, they had to groups like the Peruvian Shining Path or Mexico's Movimiento de Acción Revolucionaria (MAR). The global nature of left-wing terrorism in this period contradicts the idea that left-wing terrorism was a phenomenon unique to former Axis countries. There was no shortage of pop-psychological analysis during the 1970s and 80s that contended that the groups like the RAF were part of a generational attack by youth on their fascist parents. Part of this justification originated from the groups themselves as they framed their terrorism as a response to fascism which they contended had crept its way back into power in the West. The idea that "Papa war ein Nazi" has proven to be an enduring one as it both explains left-wing terrorism as a youthful fling with radical politics and gives it a backhanded justification. It is not uncommon in the contemporary German left to find sentiments claiming that groups like the RAF and RZ saved the FRG from falling into a fascism 2.0.

The problem with this reductionism is that the biographical details of a lot of these terrorists does not sync up with a picture of fascist parents and youthful counter-reaction. Meinhof was raised by her mother Ingeborg and her lodger Renate Riemeck after her father's 1940 death. Riemeck was not only an outspoken Christian peace advocate, but also rumored to be a lesbian lover of Ingeborg. Gudrun Ensslin, the real brains of the first generation RAF, was the scion of a rather pious Lutheran family while Baader's family background was rather unpolitical. There were exceptions such as the Italian Mario Moretti, but it was more typical that the parents and authority figures for these future terrorists to have been in some ways at odds with fascism. While there were a number of ex-Nazis within positions of power of the FRG, very few of them had direct family ties to these terrorists.

By the same token, reducing left-wing terrorism to an Axis problem also sidelines the significant presence of non-Axis members from the global South in these groups. The Venezuelan Sánchez was incredibly important as a nodal point for would-be Western European terrorists. The close identification of these groups with the Israeli-Arab conflicts also brought them into contact with the various intelligence services of the MENA region. This caused a number of these groups to be caught up into intra-MENA conflicts their leadership never fully appreciated as seen in the semi-comic denouement to Sánchez's OPEC raid where Carlos had to negotiate an end to the crisis he had initiated. Groups like MAR and the Shining Path were no less dramatic than the RAF in the 1970s and 80s, but they did not have a fascist generational backlash to justify their actions. While these Western European and Japanese did cite fighting the legacies of fascism as one of their rationales, the presence of other left-wing terrorist groups from countries that did not have a history of fascism suggests that there were other factors at play pushing these two decades of terrorism than the events of 1939-45.

A quick note on the latter point: it likely is significant that these nations were formerly fascist. Generally the most effective resistance against fascists comes from communists... but either way there were radical leftist militant groups around the world. In the 70s the USA had the Black Liberation Army, for example. So it's not as if only formerly fascist developed/Western/capitalist countries had groups such as these, if you meant in the manner of militant leftism.