Approver Comments:
It does indeed appear that Szlomo was deported to Chelmno in September 1942. And Baszejwe was sent on the same transport (as well as living at same addresses as Szlomo). So, she was almost certainly a relative. However, Baszejwe was 42 years older than Szlomo. So, she may have been his grandmother rather than his mother (though I am not seeing another older woman in his home).
As for Bill finding someone with the name Szlama Ajzenberg in the Lodz Jewish Cemetery, this does not tell us much. Without a birth date, this is likely one of the other Szlama Ajzenberg's who were living in Lodz. If our student was sent to Chelmno, he would have been killed in the gas chambers there. There would be no grave for him in Lodz.