Zvi Litvinoff is sort of a curious case (note: that's not a Benjamin Button reference). Sometimes he seems like the villain—and, really, if you twisted our arms and said this book had to have a villain, he would really be the only sensible option. But, for the most part, Zvi seems like a pretty sweet guy. And though technically he does do one pretty bad thing (betraying his friend Leo and claiming to have written The History of Love), he feels really, really bad about it. The guilt probably kills him.
Not only that, but it's only through him that Leo and (young) Alma end up getting together. So maybe we should be thanking him for claiming The History of Love as his own. The book ends without giving any hint of how the characters might judge Zvi's actions, but it's hard for us to imagine Leo being angry with the guy—especially since, in the end, he got the book back and was totally psyched.
It's also important to remember that Leo and Litvinoff are not only old friends, but have shared much of the same suffering since leaving Poland. Litvinoff lives alone for many years in a strange country (Chile, in his case), gradually learning that all his friends and family were killed by the Nazis. When he finally meets his gal Rosa after so many years of solitude (not quite 100, but it's close), it's perhaps understandable that he would feel insecure about her loving him. (That's not to mention that she's much younger than he is.) So, he does something drastic to keep her by his side.
Another thing we notice is that, in the end, Leo is able to give up his solitude in favor of a life-long partnership with Rosa. Maybe we're supposed to infer that, in doing so, he surrenders his ability to write, so he has to steal Leo's work. But that's just a thought.
Finally, does Litvinoff represent anything on an allegorical level? He almost seems like Leo's guardian angel, in the way that Zvi stashes Leo's obituary in his breast pocket "for the rest of his life" to keep it "from becoming real, so that he could buy a little more time—for his friend, for life."