The battery used in these speakers is 11.1V 4400 mAh Lithium Ion 3S2P 18650 battery pack. It consists of 6 cells total. The battery pack is protected by an internal PCB board. You can build your own, but I highly recommend purchasing a pre-assembled pack made with high quality brand name cells. Here is one.

The original Big Blue Party connector is 2 pin JST-XH 2.54mm 2P. There are many places where you can obtain one. You can even get it on eBay with attached wire leads. Pay attention to the wire polarity! Many vendors sell these connectors with wires attached in reverse from Big Blue battery. You can always reuse your old one though.

The original Big Blue Party connector can be attached by simply soldering the wire leads to the battery wire lead. Once again, pay attention to the polarity!

The Big Blue Party 360 connector is 3 pin JST-XH 2.54mm 3P. There are many places where you can obtain one. You can even get it on eBay with attached wire leads. Pay attention to the wire polarity! Many vendors sell these connectors with wires attached in reverse from Big Blue battery. You can always reuse your old one though.

The Big Blue Party 360 connector is much more complicated. You will need 10K NTC thermistor in order to make it work like the original battery. The recommended one is an axial mount type. Once again, these are carried by many vendors, here is one of many. You will need to attach the connector to the battery pack as follows (see attached diagram):

Positive (red) wire on the connector will connect directly to the positive (red) wire on the battery pack.

Middle (white) wire on the connector will connect to the one side (doesn't matter which one) of the NTC thermistor. Other side of the thermistor, will connect to the negative (black) wire on the battery pack.

Negative (black) wire on the connector will connect directly to the negative (black) wire on the battery pack.