I love the new Microsoft Reading List. Does anyone know if there is a way to share the reading lists between your Windows desktop and the Windows phone?
Not yet but hopefully when Windows Phone 8.1 is released next year. Also note that you can add (and vote for) suggestions over at the official user voice site:
Did this solve your problem?
Sorry this didn't help.
Great! Thanks for marking this as the answer.
How satisfied are you with this reply?
Thanks for your feedback, it helps us improve the site.
How satisfied are you with this response?
Thanks for your feedback.