1) In the old Perfect Browser, go to Bookmarks > Options > Export Bookmarks to HTML.
2) Tap Downloads / Files (blue arrow). Find 'Perfect Browser Bookmarks.html' from the list. Tap 'i' next to it.
3) Choose 'Open in...' and select the new 'Perfect Web'.
From Perfect Browser Pro:
4) Go to Bookmarks > Options > Import Bookmarks. Tap 'Select bookmarks html file' > Select the 'Inbox' folder > 'Perfect Browser Bookmarks.html'
5) Tap Import. You're done!
iPad Users, don't forget to enable 'Always Show Bookmarks Bar' in Settings to see the bookmarks bar.