The definition of conspiracy being thrown around here is the very specific legal term. When two or more people collaborate on a criminal enterprise, there is a conspiracy.
Collaborating to defeat Nazi Germany is not a conspiracy. Collaborating to produce false evidence in a trial is a conspiracy. If that false evidence leads to the execution of a defendant, those producing the false evidence can be tried for conspiracy to commit murder.
This isn't hard, and it isn't a trick question.
You have accused people of forging evidence that resulted in a lot of people being hanged. Kaltenbrunner probably isn't the best example, because he was charged and found guilty of several counts, not all of which were directly related to the extermination of the Jews or Roma. However, there were several people who were hanged whose only capital offense involved putting people into gas chambers. (I'll put forward the name of Irma Grese as an example, but there are lots of others.) If there were no gas chambers, these people were wrongfully convicted and wrongfully executed. Furthermore, the nature of the evidence used in their conviction was such that it had to be true, or had to be forged. Since you don't believe that the evidence is true, you must believe that it was forged. The people who did so are, therefore, guilty of conspiracy to commit murder.
Care to name any names?