It is possible to "cheat" the mobile into thinking that is connected to battery, while it is in fact connected to external power supply
How to use phone without battery provides instructions on doing it and has a 4 pin configuration as on your device. I am not elaborating on the details involved as
- This is not a standard method and more of hobbyist/ DIY project
- I would not recommend any methods that are different from OEM specified. Battery Charging is fairly complex and attempting to replicate by such methods can cause harm to battery/ battery life / device besides being a safety hazard.
To give you an idea of what typical OEM battery charging does and what you would not be able to implement (since you don't know how the drivers are designed):
The IC (fuel guage IC) monitors a voltage drop across a small current sense resistor connected in series with the battery to determine charge and discharge activity of the battery. Compensations for battery temperature, self-discharge, and discharge rate are applied to the capacity measurments to provide available time-to-empty information across a wide range of operating conditions.
Battery capacity is automatically recalibrated, or learned, in the course of a discharge cycle from full to empty. Internal registers include current, capacity, time-to-empty, state-of-charge, cell temperature and voltage, status, and more.
What does it mean if you can't implement these features (listed above)?
Li-ION batteries have four stages of battery charging- Constant Current,
Saturation (Constant Voltage), Ready (No Current) and Standby. The battery charging hardware and OS is tuned to ensure that the battery spends required time with appropriate Voltage and Current levels in each of these stages to ensure proper charging
Charging directly by external power supply cannot achieve this resulting in Short term- Battery not delivering rated capacity for every charge and Long term - reduced life of battery. To understand more about Li Ion charging, see BU-409: Charging Lithium-ion
Related: For getting an understanding on the possible reasons for have 4 pins, see Why does this mobile phone have 4 terminals. Unless you have the specific pin out diagram for your battery, you can't be sure of the reason for fourth pin (my guess is NFC related). This is the only source I am aware of for getting pin out diagrams