I want to have a 10Ah battery (3P - 3,7 V, charging voltage is 4,2 V), but it would take too long to charge via existing (module) charging, that's why I want to add an additional charging port, connected to the battery to allow for faster charging.
How do I make it happen?

I have a module that has this charging specs:
- Charging voltage = 4,5 - 5,5 V
-Charging current = 350mA

There's a PCM between module and battery, specs are:
- Overdischarge protection at 2.9 V
- Overcharge cutoff at 4.25 V

 

Check spec sheet to find the maximum recommended charge rate for one cell, then buy a charger that will supply that current X3 and that has the necessary charge control built in.

 

The TS needs to understand that faster charging has costs, the first cost being shortened battery life, the second possible costis a violent battery failure. MOST of those lithium battery fires we read about are caused by incorrect charging, either at an excessive rate, or past the specified voltage. THUS you need to understand the maximum battery charge voltage and also the maximum battery charge rate specified.