I have done this before, using a commercially-available adapter for connecting POTS line speakerphones to PBX (digital) phones through the handset jack. This is one example:
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can find them cheaper elsewhere. I made a 2.5mm-to-RJ-9 adapter- the RJ-9 (or RJ-22) is the thinner version of the RJ-11, and requires a smaller crimp tool. You may find it easier to take a handset cord apart, but those wires are really thin to be really flexible- tough to solder and work with. But, the idea is to feed the headphone signal to pins 1+4, and the mic to pins 2+3. I found that the polarity is critical, so experiment before finalizing the solder job. In fact, the one I built worked with my cell phone would not work with my cordless phone because the polarity was opposite. Of course, there are other cell-to-phone adapters commercially available out there, for ~$130. What's your budget? Totally DIY, less then $50? or more? The least cost would need a telecom transformer made for this sort of current flow. You have to be able to inject DC along with the audio signal, which may saturate an incorrect xformer. Some kind of amplifier and hybrid would be needed as echo return would be a problem. It gets more complicated to build it correctly, but not too bad. A classic 2 op-amp hybrid would do the trick. Google it and you should find several examples. Balance it just right, and you should be fine. Hope this helped.