Note - You will need basic electronic skills to build the project in this tutorial. You will also need to do some research to verify whether or not it will work with your phone and what connectors you will need. Use this information at your own risk; do not complain if it doesn't work for you. Only use as prescribed. Your mileage will certainly vary.
Let me state it again since some folks have ignored it in the comments. I am NOT providing a specific schematic, details on the connector for any particular phone, or more details on how to hook this up. It is an extremely simple circuit if you've got the right skills and knowledge and the ability to use a search engine to look up the details for your particular phone and verify that it'll work with whatever handset you can get your hands on. DO NOT ASK!
Here’s an interesting retrohack which is actually more practical than it seems at first glance – connecting an old telephone handset to your cell phone.
It’s been done before, primarily with Bluetooth. Many of the mods just repackage a Bluetooth headset by removing the handset’s original microphone and speaker and putting the Bluetooth mike and speaker into their locations with whatever extra wiring is required. A few use the original handset’s mike and speaker and connect the wires to a Bluetooth module. But this version is non-invasive (doesn’t change the handset) and is corded.