Well, I'll post the final trace of the circuit in a short time (aka.. when I can finish it), even if some details does seem to not match (starting current, final current) - I think my multimeter is defective, especially in current mode, its serie resistance in affecting the measure.

Yes, at battery voltage 4.2 it is still pushing 13mA - the battery is able to reach 4.22V (and beyoind) but I stopped the charge and did not yet measured the current.

Charge current is slow though, limited by a 10ohm resistor; it starts at 180mAh and goes down in a strange way.

The RED led goes off.. the control ciruit for it is a dirty PNP with the base connected to the input line for the current going to the battery. While the charge current decreases, the base voltage increases until it reach 4.3 - at that moment the PNP is slowly turned off, because base voltage must be 0.6V (depends on transistor model) less than Emitter voltage (which is connected to +5).. a dirty trick :\

The only good part, is the TL431, which safeguard the final battery voltage and block it from going over 4.25V by turning off the base of the final transistor.

The first mod would be to half that 10ohm value, and thus increase the initial charging current. I'll also tweak the output network o lower the final voltage threshold to 4.22, which is more than reasonable - I might check the final voltage of the battery when charged by the original Nokia adapter.

When the RED led is off, the battery is still far from being fully charged - mine the red led is dimming until you can see the red "dot" inside the green led.



Full size Diagram

If you need the schematic file to use in LTspice just drop me a private message - at now still I don't want to post it straight to the public, I don't feel satisfied yet (accuracy is somewhat random..).