A page on the website of the International Humanitarian Fact-Finding Commission (IHFFC) states
One of the most important characteristics of the Commission is that it may conduct an investigation only with the consent of the parties involved.
Let's say that Country A recognizes the IHFFC and asks it to investigate a conflict between Country A and Country B, which has also recognized the IHFFC and declared so accordingly.
If any other parties are involved, they must give their consent to any investigation. However, what is the definition of "involved"? If Country C lent arms to Country B that were used in the action under investigation, is it counted as "involved", or would it have to take direct military action for it to be considered "involved"?