Im sorry anon, but no.
In fact, you have to find a way to dispose of this safely. This is practically now a bag filled with acid ready to burst that might react if it comes in contact with water or oxygen.
If you want to play with your PSP, you will have to find a new one that can be accomodated to your PSPs model, or say goodbye to your PSP.
I pretty much lost mine this way, mine inflated until it stopped working, then whenever i tried to find a new one the only ones available would be second hand used batteries, sometimes they weren't even for the same model. This is important, some batteries for some models are bulkier, so they don't really fit and hold in place properly.
Im not even sure if they still manufacture some of these, unless it is from an obscure chinese/taiwanese factory.