Can I work with architect in New York State to prepare a project for a house that is located outside of the state (i.e. New Jersey, California, Puerto Rico)

You can work with an architect licensed in New York on out-of-NY project only of that architect forms a joint venture with an architect licensed in that State or territory (i.e. New Jersey, California, Puerto Rico). In order to get a construction permit in that state, you are required to submit your project to local building department and get it approved. That could be performed under supervision of both architects.