Update (Dec 20, 2016): We updated iAnnotate PDF to include an automatic file transfer tool designed to move your PDFs from iAnnotate PDF to iAnnotate 4. More about that can be learned here. If you do not want to use the automatic transfer tool, you may follow the suggestions below.
 

Open In...

If it's not many, we suggest using Open In... to move files into the new app. The limitation there is that you can only use Open In... for one file at a time.
 

 

Cloud Service

If you have a full Library of documents, you will want to start by transferring your files and folders to your local computer by using the Send to iTunes command. Once your files are moved into iTunes, you can sync them to the cloud to one of our four supported cloud platforms. All of our supported cloud platforms (Dropbox, OneDrive, Box, Google Drive) have desktop apps that will create a synced folder on your computer. Once you have that folder, you simply need to drag the files and folders from iTunes File Sharing into the synced folder.

Once that is done, create a connection to that cloud service and you will see all of your documents ready to go.

 

iTunes, no cloud

You can also move files using iTunes if you prefer to not use the cloud. Start by using Send to iTunes, as described above. Once the files are in iTunes, drag the files to a permanent location on your computer (such as your desktop). Switch to iAnnotate 4's file sharing area, and drag the files and folders into that section. Once that is done, add iTunes File Sharing as a Storage area in the app.