Electrical – Creating a protected 18650 cells pack

Cells in devices that you do not wish to be a flaming ruin MUST have protection.
Having protection circuits does not guarantee it will not happen.

Cells without protection are intended for use by either manufacturers or experts or enthusiasts who add their own or for suckers.

Whole device protection and cell protection are complementary and serve overlapping but different roles.

4,000 mAh 18650 LiIon batteries are ~~~= 99.9% +0.1% - 0.0% sure to be rubbish.
ie not just < 4000 mAh but << 4000 mAh and low quality.
The people who bogus label cells

• almost never feel an obligation to use the best cells they can and

• almost always decide to add injury to insult by using junk as well as lying.

Real world experience shows that the value of 'almost' is very high in both cases.

Higher capacity cells can usually be fitted OK.
MUCH higher capacity will lead to long CC tails and overcharge but not an issue here as mAh_new is < to << 4000 mAh.

ADDED:

Notice that in this ad and all their other ads they ALWAYS show non-brand-label views of the battery.

However, you may find that the racing stripes and general colour scheme a good match for the well known "Ultrafire" brand batteries. This may in fact be a real brand and these may be real examples of it BUT you can buy empty shrink wrappers to apply to the battery of your choice with this (or other) branding on it , so caveat emptor. Better nullius emptor I'd hazard.

These ones are a stunning 6800 mAh - a steal at the price. Available here

You'll find others similarly arrayed here and
here - 3000 mAh and 4000 mAh and

6800 mAh !!!!!!!!!!!!!!!! {again}

and unspecified but with GENUINE CREE 2000 lumen {so 20+ Watt} flashlight for $9.27 and
only 4000 mAh and
that's better - 4200 mAh
and .............

Flee!

Can your 2s charger not charge in normal or 'unbalanced' mode with the 3 wire balance connector not connected? Almost all chargers do.

So why balance charge your 2s battery? The TP4056 chips should ensure that they each charge to the correct 4.2 volts and therefore will be balanced. Or will th TP4056 not work when charging in series?

Even if you connect the balance wires, it should work. All the balance wires do is measure the voltage and then at the end, or near the end of the charge, bleed small current from the higher voltage cell and then recharge the battery up to 8.4v. So can you discharge a small current (usually less than 300mA) from the TP4056 connector? If so, then I believe that it should work. If the TP4056 connector doesnt allow you to measure the cell voltage, then the charger won't even start.

However, I have no experience with the TP4056 so watch it closely if you decide to go ahead!