I believe this is the same student who signed the album, because his birth date fits exactly within the window of school 21B, where he went to school. Mordka/Mordcha also have extremely similar sounding names, with the alternate spelling likely being the reason their names are different in the Lodz database. I believe they are the same student, because of the same Hamburgerstrasse addresses, as well as the date of his new address being within 3 days of the unlabeled note/date on Mordcha's page in the database. He likely was born sometime between February and November of 1930, making him a common age when the album was signed.
Since we have two identities in the catalog to deal with, I think I found the connection between the two. Mordka's entry has him as an ABG, or a change of address, to Alekshof, which is missing from his entry. Mordcha, has an "Alexhof" address listed, as well as the date 21.12.42, which, considering the fact it is three days after the date on Mordka's entry, makes me believe that the unmarked date is the same event.
I also found both of his relatives by means of a simple last name search, then selecting all of the results and checking them with Mordcha's, and I found two matches. One is probably a mother, who's birth date would fit the timeline of her being his mother, and the other is a brother, who was born about two years earlier. They both have the same timeline of addresses as well.