Coupling electret microphone input to linear audio output
Having looked at the specs, it looks straightforward. With one caveat, it should be possible to connect the differential output lines of a speaker out to the differential mic inputs.

The speaker outs want to drive a lower impedance, down to 32 ohms, but they will be fine with a higher one (and note that in the table, no maximum impedance is listed: the max value is given explicitly as a dash). The output impedance of the stages, though not given, is quite likely low, which is a good thing from the perspective of driving the mic input.

The one slight problem is the mic input sensitivity. The differential output can go 2.2 volts peak to peak. This corresponds to 1.1V amplitude, which is about 780 mVrms.  The microphone input is cited as taking only 740 mVrms while distortion stays below 5% (at the minimum gain, 0dB). I.e. this output level is already in the territory of objectionably noticeable distortion and can be taken to be the limit of how hard the mic input can be driven while staying reasonably clean (if not for hi-fi than at least for telephony).

The two figures are quite close, but, all the same, would probably make sense to attenuate the speaker output somewhat to have gain headroom in the mic input, even when the speaker out is producing maximum output.

For the differential hookup, you can make a voltage divider circuit using three resistors. That is to say, the output circuit goes from the P output, then across R1, R2, and R3 and returns to the N output. R1 and R3 are equal, and the differential mic input is taken across R2.

A good total value for the divider (R1 + R2 + R3) might be something close to the impedance that the mic would have, around 2K. The speaker output can certainly drive that since it goes down to 32 ohms, and as an source impedance to the mic input, it matches the "typical" value, so it's not an impedance that the input will "hate". If R2 is chosen to represent 20% of the total resistance, then the roll-off will be about 14 dB.

The datasheet's circuits show some capacitors for RF filtering and transient suppression diodes for ESD protection applied to the differential lines, in a very similar setup for either input and output. Those features be replicated in this cross-coupling.