We are trying to achieve real time transcription during a person-to-person phone conversation. What is the cheapest/expeditious way of achieving it?

There might be some mobile app that does this. If not find some app that will actively record and send your calls somewhere and try to get that setup with some transcription service.

Doing it in real time might be problematic since I think most call recorders just record directly to the device. If you installed teamviewer on the phone or some alternative (assuming it is a smartphone) then you could monitor the calls and send that data to a transcription service from another device.

Still there will probably be some slight delay depending on internet speed so it won’t really be in real time.