Help me with a 4S1P for vacuum cleaner please
The module is a 'PCM' (Protection Circuit Module). It disconnects the battery if the voltage goes too high (overcharge) or too low (over-discharge), too much current is drawn (short circuit etc.), or the temperature goes too high. It does not do balancing or charging.

P+ and P- are the output terminals. B- is battery negative (negative terminal of lowest cell). Between B- and P- are a pair of MOSFETs which act as a switch to disconnect the battery when a fault is detected. V1, V2, V3 and V4 are the positive terminals of each cell (from lowest to highest voltage). V4 is connected to P+, so it has a thick wire to handle the battery current, while V1-3 are thinner because they only sense the cell voltages.    

The circuit looks something like this (simplified):-







simulate this circuit &ndash; Schematic created using CircuitLab

To replace the cells you just have to unsolder the old ones and solder in the new ones. However there are two issues with DIY cell replacement:-


The cells must be balanced for equal voltage (within +-0.01 V) when fully charged. Since the PCM does not have balancing capability you must do this yourself. Easiest way is to fully charge each cell individually on a single cell charger, making sure the long-term resting voltages are the same. This makes connecting them up more dangerous due to the higher stored energy, so be careful! Keep all exposed terminals covered with insulation tape except for the one you are working on. 
Cells are usually connected together with spot-welded nickel straps. If you don't have a spot welder then it is possible to solder wires to them, but unless you have vast experience at soldering battery packs there is a very high risk of damaging the cells and/or not getting a good connection (I do have vast experience, and even I avoid doing it if possible). 


Due to these issues I don't recommend rebuilding the pack with individual cells. Send it to a professional rebuilder or buy a new battery.