Sergei says, “I am happy that my words have taken effect.” Why does he say so? Is he right in saying this?

When Sergei got Lushkoff to work for him the first time, he wasn't a willing worker. But after chopping wood for Sergei and helping him move houses, Sergei noticed that Lushkoff had developed a willingness to work. On seeing this, Sergei felt content that because of his timely advice ,Lushkov could get rid of begging and has become financially independent.He is now on the right path and that he wouldn't have to beg again for a living. If Sergei had not helped Lushkoff, he would still be telling lies and begging on the streets.

Sergei thinks that because of his timely advice Lushkoff could get rid of begging and is financially independent. He is right from his perspective because he doesn’t know that it was Olga who chopped woods for Lushkoff. Anyway, the end result is Lushkoff’s life is back on the right track. And there is a saying, “all is well that ends well.”