Q. How do I transfer my EndNote library to Mendeley?

To do this you need to export your EndNote library as an XML file and import it into Mendeley Reference Manager

Endnote Desktop (20):

• Open Endnote and select all the references in your Library (Ctrl +A)
• File > Export 
• In the dialogue box choose a file name and place to save the file on your computer.
• Save as type: XML
• Output Style: RefMan (RIS) Export (You may have to find this from the 'select another style' option) 
• Make sure the 'export selected references' box is ticked
• Click save to create the file.

Then on Mendeley Reference Manager: 

• + Add new button (top left) > Import Library > EndNote XML (find the .xml file you have saved) and click open

NOTE although this worked, during testing I exported 378 references from Endnote but only imported 365 to Mendeley. Some were lost along the way. 

If you export your whole library then it will not carry over any folders, so it might be worth doing it in batches so you can recreate the folders on Mendeley.