The original restaurant "Le Belvedere" closed in 2013, changed owners in 2014, and is now open as "O Belvedere" as of 2015. It's unclear as to whether or not it still operates a shuttle... my guess is no, but they can be contacted at +689 89 403 403 or via email at email@example.com. Website is http://www.o-belvedere.com/en/
Thanks for the updates. I will add them to the page.