What does exactly mean...?

Rating: Null/10 (29 May 2005)

Hi everyone, fans of Memento! I love this movie, and I've watch it a lot of times, but I still have a little problem: I'm from Spain, my English is far from perfect, and I can't understand why Lenny calls Teddy after beating Dodd. I mean, I know he calls him because he sees the name written down in the paper he's carrying in his pocket. But, here comes my problem: what mean "put him onto Teddy"? I don't know, the Spanish translation gives something like "ask for Teddy" ("preguntar por Tedddy"), but is this the real meaning of the sentence? Can anyone please give me an explanation of the meaning of "put him onto Teddy"?
(thanks in advance, sorry for my awful English)