Pre-amplifying an electret mic already in use
The DC component from the phone will continue to supply the electret mic capsule.
As you show, the connection between the mic capsule and the phone remains intact. 

It is trivial to block the DC component with a simple capacitor. A value between 1 and 10 uF would be more than adequate for the expected impedances and low frequency response needed. I would use a capacitor rated at least 5~10 V.

Then you simply need a "mic preamp" which is just an amplifier stage of perhaps 40dB gain (depending on the signal level from the mic and what your alternate destination needs.  There are scores or hundreds of examples online of op-amp circuits which provide varying amounts of audio gain. Many are specifically designed for low-voltage battery operation.

Note, however, that computers and recorders typically also have mic-level inputs, so you may not actually need any gain here. Simply using a capacitor to block DC (in either direction) would be something I would try first, before going to the trouble of making a gain stage.