Ok got the cell riged into a slim battery case
And here it is powering the PSP
Battery statis with it unpluged
And with it pluged into AC

PSP is a little confused
As i post this it is telling me the battery is fully charged at 100%
and still the power light is orange and it reads as charging
i'm guessing the PSP can't tell exsactly how much power this cell holds
and i will have to do a timed test to see just how long it will last
My standard battery lasts 2:35 with screen at max and running the demo loop in Armored Core 3 Portable.
Looks like the next step is to fit this monster into the PSP it self