Originally Posted by
Analise
I bought a USB connector (it's not lightning speed) from a discount store because the iPhone cable stopped working (may have been bent too often). May I assume I can use that to charge the power supply overnight?
Ok.

Lighting doesn't refer to speed in this context.
Lightning is Apple's trademarked name for the proprietary connector it uses in all its mobile electronics. The cable that came with your phone converts a standard USB connector to a Lightning one. You can buy third party ones too.
The battery you buy will most likely come with a USB to micro-USB cable for charging the battery itself. You then just plug your Lightning cable into the battery's USB port, and into your phone.