In order to move from Papers 2 to ReadCube Papers, you will need to go through Papers 3 first.
First, you can download Papers 3 here. Upon launching it, a free 30-day* trial will begin. During this time, you can import your Papers 2 library into Papers 3 and then from Papers 3 into ReadCube Papers by using our desktop uploader.
Visit our Papers 3 Library Transfer page to guide you through the process.
*Please note, you cannot upgrade to Papers 3 as it is no longer available for purchase as of November 2018. The free trial is only meant to move your Papers 2 library.