OK, the thing is, the little jack on your cell phone is the hands free jack, which is a 1/8" jack. but not a typical one. It has (IIRC) three connections, one is the speaker, one is the mic, and the other is a common ground. Now, if you plug that right into a recorder with a patch cable, it would record the other person’s voice, yes, and you might even be able to hear it through the recorder’s speaker if it has one and owrks like that (I imagine most do) but you will have no awy to talk to him.
So, you need to get a 1/8" splitter cable, that turns the one male end into two female ends, and then buy another 1/8" patch cord. Run the patch cord to the recorder, and use the other female jack for the hands free set. The only problem I see with this is the recorder might not record what you say. I’m not sure if the signal from your voice will “loop back” through the splitter into the other end to the recorder. Seeing as they are designed for the signals on both lines to be coming from the same spot, not for one to be coming from one end and the other from another, it might not work. But it might be worth a try.