There are several young men in the Lodz Ghetto Inhabitants database who are potential matches for the boy who signed the album simply as "Abgac."
Probably the best match based on sound is Aron Dawid Obcas. He was born in 1933 and was a student. On January 26, 1942, he was relocated, probably to Chelmno, since there were 14 transports sent there during this time (see secondary sources).
Otherwise, I believe that the three boys with the last name Abzac are also good matches, assuming that the database transcription was imprecise. Both Jakub and Abram were registered as students. However, Abram was a tiny bit old for school #12A. It's worth noting, however, that in the database of Jews deported to Chelmno in 1944, Abram is listed as being born in 1928. So, he may be within the proper age range for this school.