This thread is for those who happened to be saddled with a power bank that takes charge but do not charge our devices properly. It's an easy task to repair it and even make it better. And you may only need to do the easy part. Here is what I did:

I had a 2800mah power bank that charges my phone for about 35 mins before indicating low power and goes off after 15 mins. It really is bad. I gathered the following items:

2000mah (Blue) or 2600mah (Green) battery cell (shown)
Soldering iron and solder (optional)
The low charge power bank
Flexible wire.

1. Take the power bank apart.

2. Disconnect its own battery from the B+ and B- terminal on the USB circuit. Alternatively, you can remove the B+ and B- wires from the terminals of the batteries instead if you don't want to solder it yourself.

3. Now, using the flexible wires, connect the new battery (or batteries) to the B+ and B- terminals. Remember, the + of the battery goes to the + of the power bank circuit. This is where you need the soldering iron.

4. If you want to upgrade the power bank, increase the number of battery cells by connecting it in parallel (I.e. side by side) not series (I.e. one in front of the other). This is very very important (shown) I upgraded mine from 2000mah to 5200mah in this way.

5. Fit the circuit board and its USB ports as well as the batteries into any case of your choice. To prevent much heating, make sure there are spaces and vents in the case.

And you're done.
I used mine to top up my battery from 0 to full twice in the past two days to test it. It gave out on the third charge. The more the batteries in parallel, the higher the charge stored. However, notice that it would also take longer to charge than the former state.