Measure the phone output signal to calculate the required attenuation. Apparently each phone might produce an slightly different signal.Build a pad (essentially a voltage divider) able to attenuate the signal to mic level,
Convert the pad output (high impedance due to the two resistors) to low impedance so that it loads the receiver circuit as much as the original mic. This can be done with an op-amp buffer amplifier.
Center the signal around 1.5 V ideally, but anything from 0.5V to 2.5V would do according to the manufacturer
You have used this board with the mic. and were happy with it?I may want one of those. How close to the mic. do you have to be?
It won't hurt the headphone outputs to have higher impedances on them.
No battery is necessary.