I left out the following questions. Thank you very much, Writeacher.
1) First, the organization collects information. When it has proof that a person is a prisoner of conscience, it hands over that person’s case to a local group.
2)This group send (or sends?) letters to governments and raise money to help prisoners (or the prisoner). This (group) will only be satisfied when they manage to set free all the prisoners.
1 - OK
2 - This group sends ... prisoners. This group will ... set free all prisoners.