After the Soviet invasion to Czechoslovakia in 1968, Kulka immigrated to Israel. He continued his research activities at the Hebrew University and at the Yad Vashem institute resulting in a first-time-in-history study relating to the significant participation of Jews from the Czech Republic and Slovakia in World War II for the liberation of Czechoslovakia: ""Jews in Svoboda's army in the Soviet Union" and "Jews in the Czechoslovak Army in the West"".