Send one link, and whoever gets it is in. From then on you all see the same list — every change appears on the other phones right away.
Type the first letters and pick from the suggestions. Things you buy often turn into favourites, so next time it is a single tap. The more you use it, the less you type.
Everyone in the list sees what is already in the cart. You can even split up in the shop — two people, two ends of the aisle, one list, no duplicates.
When a member starts shopping, the others get a notification. Enough time to add the thing you forgot before they reach the till.
Nothing. The app is free and shows ads. If they bother you, you can switch them off with a one-off purchase.