Ohh, you're right, I never noticed that but I saw the episode many times and indeed it's never mentioned.
I think a reason for that is he basically collaborates with the boys till the end of the episode, making them think he's not onto them, until the final shocking reveal.
An episode with such a similar reveal is a friend in deed, he also collaborates with the commissioner until the end, and now I think about it, I don't remember the heritage motive being mentioned either, after the commissioner's wife died.
they had to because the one kid (blond) was put on notice by his father (after hearing he got another girl pregnant) that if he fu$ked up one more time, he was going to be cut off from the purse strings. The Professor was going to expel them for cheating so they had to kill him