Animation Shop no longer ships with PSP after PSP 9. However, if you have a previous version of PSP which included Animation Shop, you can use that version of Animation Shop with any version of PSP. To start Animation Shop from within PSP, I have provided a small script based on a function written by Gary Barton. Bind this script to an icon using Customize in PSP, and then place that icon on a toolbar or menu so that you can start Animation Shop at the touch of a button. Click here to download the script.
In this script, which must be installed in a Scripts-Trusted folder, I have used the path to the Animation Shop executable as found on my system - if your path is different, edit the script, changing the path in line 42.
If you need help binding the script to an icon, visit my Using Bound Scripts in PSP tutorial.