Each Kindle file is locked to a single device, i.e. it contains one PID. If the file came from your Kindle 1 it will have the Kindle 1 PID in it.
However, if you go to the "Manage your Kindle" page at Amazon you should be able to redownload all (or almost all) ebooks for a new device. If you have a Kindle, the file can be downloaded directly to your PC and it will have the Kindle PID in it. If you only have a iPhone, the files always go to the iPhone (and will contain its PID).
Note also that some Kindle ebooks don't have DRM, and so don't have a PID at all.