Well to quote Presto’s shopping page:
The battery connector can be used to power Presto with batteries that provide between 3V and 5.5V. At the lower end of that voltage range, you’ll start to see dimming of the backlight and less vibrant colours. We’d suggest using a chunky LiPo, or a 3x AA alkaline battery pack - check out the extras for some options.
So you basically need a battery delivering 5V into the JST PH 2mm connector. The pimoronis seems to be the easiest solution for you. You will need a charger aside though.
And if you mean using the battery connector to deliver power without battery, it already have been answered in this thread :
I hope this helps and I understood your question correctly.