Never had an issue with sharing a note, sorry.
But FYI my favorite grocery list app is Anylist, which is free and has a huge database of items and can categorize list items (eg produce, dairy) for easier in-store shopping, derives shopping lists from imported recipes (browser extension pulls recipes on command from websites), and more. It lets you share lists for free, or make lists editable by all family members ($12/yr for family), with Mac/web/iOS access. The pay version lets you assign stores to items or lists, offers location-based reminders… and more. Your list doesn’t have to be groceries - I use it for packing lists and items I need to buy at the hardware store - but that’s where it shines.
