Haya was born on January 1, 1923 in Lithuania to Rachel and Yaakov Srulowitz. The parents were Zionist and made aliya in 1935 to Ramat Gan. Haya began her studies there, and along with her older sister Nehama, joined the Beitar movement. The two sisters, inspired by a nationalist spirit and love of the People and Land of Israel, were very active in Beitar. Two years later, when the family moved to Kfar Saba for economic reasons, they would continue their activities, bicycling to Ramat Gan and back, despite the distance and effort.
In 1940, she started working in a diamond factory, learning diamond-cutting and meeting her supervisor, Tzvi Moritz, whom she would eventually marry.
This was a tumultuous time in the Land of Israel, with the riots of 1939-1939, the White Paper, the beginning of World War II, the retirement of Hebrew youth into the British Army, the split within IZL — the last resulting in the establishment of Lehi. These events motivated the Srulowitz sisters to take action and enlist in Lehi in 1941, then known as the Stern Gang. A friend of Nehama’s, Yehoshua Cohen of Kfar Saba recruited them (he would eventually marry her). The underground meetings mainly took place in the orchards between Kfar Saba and Raanana, in order to maintain secrecy. Haya learned of Lehi’s ideology from Yehoshua, who trained her with firearms, in one of the orchards, far from prying eyes. She was active in the Lehi branches in Netanya and the Sharon region.
In 1948, Haya married Tzvi Moritz, and they had two sons, Udi and Doron. They had numerous grandchildren in the course of time.
In 1952, they moved to Ramat Gan and Haya continued to work as a diamond-cutter in Tel Aviv. In June 1956, they made a dramatic change, moving to Kibbutz Sde Boker in the Negev, among whose founders were Nehama and Yehoshua Cohen. However, they could not get used to the routine there, so in August 1957, they returned to Ramat Gan, where they lived until Haya passed away on February 17,2000. She was buried in the Lehi section of the Yarkon Cemetery.