Most/all phones have one cell and therefore no balancing magic. Two connections do the job of connecting to the battery cell to the rest of the phone. These two are easily identified with a DMM.
If the phone works with only these two connections, then we're done; the phone will run from a bench power supply and there's nothing left to pursue.
If it does not work, then the functions of any additional connections be further explored while still never unwrapping the battery. Serial data? NTC thermistor? Something else? Fine; record that and emulate it. NTCs are cheap and so are MCU dev kits. (And if we don't have a decent-ish oscilloscope yet, then this is a good excuse to get one.)
If you don't have any real training in electronics, please refrain from giving advice like this. It can start fires, especially when lithium batteries are concerned.
Do whatever the fuck you want and suffer the consequences yourself for doing stupid things you don't understand, but don't encourage other people who also may lack understanding to follow you over a cliff.
If fucking around with lithium batteries doesn't make you pause a bit, then you're just ignorant.
Still though, could be a lot of screwing around needed to get this to work. Likely the extra wires go straight to a chip which expects to be able to monitor the voltage of the battery, and which might be alarmed by a power supply that acts unnaturally for a battery.