Why is parent not updating in ReactJS?

Question

React

Good time of the day. You need to update the Parent component.
What I do: Move a card from one column to another:

moveCard

moveCard = async (type, id) => {
    const { list_id } = this.props;

    if (type === "left") {

      const response = await moveCard("left", id, list_id); //axios patch request

      this.sub.send({
        list_id: list_id,
        card: {
          id: response.id,
          created_at: response.created_at,
          updated_at: response.updated_at,
          list_id: response.list_id,
          title: response.title,
          moved_card: 'true'
        }
      });

    } else if (type === "right") {
      const response = await moveCard("right", id, list_id);

      this.sub.send({
        list_id: list_id,
        card: {
          id: response.id,
          created_at: response.created_at,
          updated_at: response.updated_at,
          list_id: response.list_id,
          title: response.title,
          moved_card: 'true'
        }
      });
    }
  }

Ie, for example, I have 2 Column components - Column 1 and Column 2. Each of them has a Card component. I am moving the card from the Column 2 component to Column 1. A request is sent to the server via the actioncable and, in theory, the Column 2 and Column 1 components should be updated. But only Column 2 is updated, i.e. the Card component is removed from it. Very confusing, but here's what should happen.

There is also a change handler for the Card component:

moveCardHandler

let ids = [];

    this.state.cards.map(card => {
      ids.push(card.id);
      return null;
    });

    const cardIndex = ids.indexOf(data.card.id);
    const cards = update(this.state.cards, { $splice:  });
    cards.shift();
    this.setState({ cards: cards });

Rails is used as a backend.
How can the Parent component be updated?