I see, so from the cart page at:
you are using the SSL transfer to transfer the cart to the checkout page at:
did you add the ssl transfer before adding the option columns for initial and birthstone?
if so, the code for those columns would not have been included, so the options are not passing over.
you will need to delete the SSL transfer form from the cart page, delete the populate cart from form behavior from the checkout page, then re apply them so that the code will be generated for the current collection of cart columns.