using external mic to record conversations?

[Cindy B1]

I got this Olympus TP-8 Telephone Pick-Up V4571310W000 B&H Photo Video

Its a pass thru microphone. You put the earbud in your ear and there is a microphone on the outside of the earbud. This is to pick up sounds in your phone earpiece as you have a conversation. The other end goes into your recording device. You can record both sides of the conversation. I ordered it for when I have to call Comcast about my bill. Of course, my laptop only will use its own microphone, this doesn't work! It does work on my sons laptop with a separate mic input, but that isn't always available for me to use

I have the app called smart voice recorder. If i plug this into my headphone jack will it act as a microphone and pick up the conversation I have on my cell phone? Or, if I plug the microphone into the phone, but use a different phone for the call, will it simply record from the microphone?

Not sure if I asked that clearly. Basically, will my phone act as a recorder no matter which phone I use to make the call? If not, then I need to find a cheap recorder with a 3.5 input.