In searching for Moszek Argiewicz under fuzzy parameters, 4 results came up, but only Alter Mosze Argiewicz was born in the right birthdate range for his school and to have signed the album.
I was able to find Alter Mosze's family through matching addresses in the database. His family members include Gerszon (b. 1890, a likely father); Rywka (b. 1900, a likely mother); and the following youth who are either likely siblings or cousins: Fajga (b. 1920), Hinda (b. 1923), Abram (b. 1925), Szmul (b. 1930), and Szajna (b. 1933).
All were deported on March 20, 1942, during the month of daily deportations to Chelmno. The exceptions are Gerszon and Szajna. Gerszon died on February 16 (according to hospital death records)/February 17 (according to his profile) 1942 of starvation. Szajna died on February 16 (according to hospital death records and her profile) 1942 of bronchopneumonia.