Original: The International re-formed in 1923 (as the Labour and Socialist International), and was  reconstituted again, in its present form, after World War II (during which many social democratic and socialist parties had been suppressed in Nazi-occupied Europe).
Simplified: The International re-formed in 1923 (as the Labour and Socialist International), and was re organised again, in its present form, after World War II. Many social democratic and socialist parties had been suppressed in Nazi-occupied Europe).