I found by coincident the solution.
The Problem is the plugin “Role Scoper” which makes it behave strange. Once deactivated the “create new part” works and the new part actually appears on the Manage-Project-Page.
(https://groups.google.com/forum/#!topic/anthologize-users/oIGidt1axzU)
I hope that someone can fix this issue so we all can use both plugins!
Thanks a lot