There is a way to do it, but you will have to read an article first. TENSIX Consulting website found that it's possible to export data from P6 to Project 2013, but in order to do so, you will have to make sure that you have "everything linked in a downward cascading order". After this is done correctly, the export function will work as it should.
For more information I would like to recommend checking their article. You can access it through Google Search: https://goo.gl/Q5BifM
