I built a crude prototype of the two resistor voltage divider circuit using 30 KOhm and 5 KOhm resistors. When fed via my LiFePO4 battery along with my boost converter ramping it up to 19.87V, the divider voltage (voltage between the resistors) to the blue wire (center "Smart" pin) read 2.85V. Very close to predicted...
The HP Probook440 G3's battery was at 78%, so I shut it down, plugged it into my battery circuit, and then turned the computer back on. It booted right up and went directly into battery charging mode. I watch it slowly charge the battery from 78% to 100%, and then the "battery is fully charged" message appeared. Just as if the computer was on the standard HP 120VAC to 19.5VDC (actually 19.87VDC) power adapter. When I disconnect the barrel jack a message now pops up and says "battery discharging from 100%", and when I plug it back in this message vanishes.
BTW, I'm running Linux Mint 21.3.
So far this project seems to be a whopping success!
Edit: Adding that the tiny LiFePO4 battery (nominally 8Ah, and weighing only 1 Kg.) went from 13.5V (~95% full) to 13.3V (~80% full) during my test run today. This LiFePO4 battery is at 80% discharged when it hits 12.8V. 70% discharged at 12.9V, and 60% discharged at 13.0V. I'm going to add an under-voltage protection (battery cut-off) circuit set to 12.9V.