The Church Triumphant serves the saints in heaven who, with Rabbi Yeshua‘s help, have fully triumphed over the temptations of the world, the flesh, and the devil. These saints live eternally in heaven with the Holy Trinity, the Blessed Virgin Mary, the holy angels and all the other saints.
The deacons, priests and bishops who were ordained in the Church Militant bear the character imprinted by their ordination § 1583 forever. Some of them passed through the Church Suffering, while others came directly from the Church Militant to the Church Triumphant where they share with all the blessed souls the § 1028 beatific vision of the Holy Trinity.
The Church Triumphant helps the saints share in the eternal joy of the Holy Trinity, the Blessed Virgin Mary, the holy angels and all the other saints. How they help has not been revealed to us here but we are certain it will be glorious.