The battalion was organized as 125th Coast Artillery Battalion (Antiaircraft) (Gun) at Camp Haan, near Riverside, California in May 1943. Based at Camp Haan but trained at various locations throught Southern California. Staged at Camp Edwards, Massachusetts prior to going overseas in July 1944. Arrived in England July 1944. Landed in France September 1944. Participated in Rhineland, Ardennes-Alsace (Battle of the Bulge) and Central Europe Campaigns. Returned to the U. S. in March 1946. Inactivated at Camp Kilmer, New Jersey 26 March 1946.
The book you describe is a memento, commonly called a "yearbook". These proliferated in the years immediately following the war but some were published during the war. Look for a publication date. If it was published after the war, it's likely he served with the 125th overseas but still no way to be certain without accessing records.