Asia Veksler was born in 1918 in Dubossary (present-day Dubăsari, Moldova). In 1940, she graduated from the Belorussian Institute of National Economy in Minsk, securing the good position of an economist in the administration of Gomel, southeastern Belorussia. When the Soviet-German war began in June 1941, Asia was in Pinsk, Western Belorussia. With great difficulty, she managed to flee the area for the North Caucasus. In May 1942, Asia volunteered for the Red Army, and was attached to the 194th Rifle Regiment of the 51st Army. She was responsible for the monetary allowance paid to the soldiers of her unit.
With her regiment, Asia Veksler took part in the Red Army retreat in the summer of 1942, and in the Battle of Stalingrad in the autumn and winter of 1942-43. In autumn 1942, her regiment defended the southern flank of the city on the Volga River.
After the end of the Battle of Stalingrad, Veksler was promoted to the rank of second lieutenant and transferred to the administration of the rear zone of the 51st Army. With this army, she participated in the Soviet offensive in the North Caucasus and eastern Ukraine in 1943, before being transferred to the 1st Baltic Front in summer 1944. There, she became head of the financial department of the 84th Separate Auto-Transport Battalion. The citation for the Order of the Red Star awarded to her says:
"Upon joining the battalion, Comr[ade] Veksler began by putting the neglected financial affairs of the battalion in order, raising its economic performance to the level required by fiscal discipline. As head of the financial service, Comr[ade] Veksler knows and likes her job, always ensuring that the monetary allowance is paid to the soldiers on time, never delaying the payments. As a result, neither of the two inspections conducted by the Financial Department of the 51st Army have found any fault with her work."
Senior Lieutenant Veksler ended the war in East Prussia.
In 1945, before her discharge from the military, Veksler learned that her entire family, including her two little sisters, had been killed in 1942 in Transnistria. Upon returning to her native Dubossary, she made great efforts to reconstruct the story of the massacre of 18,000 Jews from the city and the surrounding area. All these people, including Jews resettled there from Bessarabia, had been killed by the German and Romanian occupiers in September 1941. In the late 1980s, Asia Veksler (now Asia Moskaliova) initiated the erection of a monument to the victims. In 1999, Asia Veksler-Moskaliova published a book titled The Tragedy of Dubossary, September 1941.