Привязка не обновляет текст после перемены мест элементов массива

Использую паттерн MVVM. Есть модель - Todo.

public class Todo : INotifyPropertyChanged
{
    public event PropertyChangedEventHandler PropertyChanged;
    public void OnPropertyChanged([CallerMemberName]string prop = "")
    {
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(prop));
    }

    public TodoUI ui;

    public bool ignore_id_changes; 

    public string prev_id;
    private string id;

    public string ID
    {
        get { return id; }

        set {
            byte b = 0;

            if (!byte.TryParse(value, out b)) { return; };
            if (ui.Todos.Count < b) { return; }

            id = value;
            OnPropertyChanged("ID");

            if (!ignore_id_changes) ui.Replace(this);
        }
    }
}

ЕстьViewModel - TodoUI

public class TodoUI : INotifyPropertyChanged
{
    public event PropertyChangedEventHandler PropertyChanged;
    public void OnPropertyChanged([CallerMemberName]string prop = "")
    {
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(prop));
    }

    public ObservableCollection<Todo> Todos
    {
        get;
        set;
    }

    public TodoUI()
    {
        Todos = new ObservableCollection<Todo>();
    }

    public void Replace(Todo active_todo)
    {
        Todo was_a;
        Todo was_p;

        Todo a = null;
        Todo p = null;

        byte a_id = 0;
        byte p_id = 0;

        for (byte i = 0; i < Todos.Count; i++)
        {
            if (active_todo.ID == Todos[i].ID && Todos[i] != active_todo)
            {
                p = Todos[i];
                p_id = i;
            }
        }

        for (byte i = 0; i < Todos.Count; i++)
        {
            if (Todos[i] == active_todo)
            {
                a = Todos[i];
                a_id = i;

                if (p == null) { return; }

                a.ignore_id_changes = true;
                p.ignore_id_changes = true;

                ////////////////////
                Todos[p_id].ID = a.prev_id;
                Todos[p_id].prev_id = p.ID;

                Todos[a_id].prev_id = a.ID;
                ////////////////////

                Todos[a_id] = p;
                Todos[p_id] = a;

                a.ignore_id_changes = false;
                p.ignore_id_changes = false;
            }
        }

        //End
    }
}

Ну и View - AllTodosPage

<Page x:Class="TodoList.AllTodosPage"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006" 
  xmlns:d="http://schemas.microsoft.com/expression/blend/2008" 
  xmlns:local="clr-namespace:TodoList"
  mc:Ignorable="d" 
  d:DesignHeight="450" d:DesignWidth="800"
  Title="AllTodosPage" KeyDown="Page_KeyDown">

<Grid Background="{StaticResource back}">

    <Grid.RowDefinitions>
        <RowDefinition Height="Auto"/>
        <RowDefinition />
    </Grid.RowDefinitions>

    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="*"/>
            <ColumnDefinition Width="33"/>
        </Grid.ColumnDefinitions>

        <Button Content="Add new todo" FontWeight="Medium" FontSize="22" Foreground="White" HorizontalAlignment="Left" Style="{StaticResource txt_btn}" Click="OnAddBtnClick"/>
        <Button Grid.Column="1" Content="←" FontWeight="Medium" FontSize="22" Foreground="White" Style="{StaticResource txt_btn}" HorizontalAlignment="Center" Click="OnReturnBtnClick" />
    </Grid>

    <!--List-->
    <ListBox Background="{StaticResource back}" HorizontalContentAlignment="Stretch" BorderThickness="0" ItemsSource="{Binding Todos}" Grid.Row="1" Name="data_el">
        <ListBox.ItemContainerStyle>
            <Style TargetType="ListBoxItem">

                <Setter Property="Foreground" Value="White" />

                <Setter Property="Template">
                    <Setter.Value>
                        <ControlTemplate TargetType="ListBoxItem">
                            <Border Name="Border" Background="{StaticResource unselected}" Margin="0 2 0 0" SnapsToDevicePixels="true">
                                <ContentPresenter />
                            </Border>

                            <ControlTemplate.Triggers>
                                <Trigger Property="IsSelected" Value="true">
                                    <Setter TargetName="Border" Property="Background" Value="{DynamicResource select}"/>
                                </Trigger>

                                <DataTrigger Binding="{Binding Completed}" Value="False">
                                    <Setter Property="Foreground" Value="Gray" />
                                </DataTrigger>
                            </ControlTemplate.Triggers>
                        </ControlTemplate>
                    </Setter.Value>
                </Setter>

            </Style>

        </ListBox.ItemContainerStyle>

        <ListBox.ItemTemplate>
            <DataTemplate>

                <Grid>
                    <Grid.Resources>
                        <Style TargetType="TextBox">

                            <Setter Property="FontWeight" Value="Regular" />
                            <Setter Property="FontSize" Value="15" />
                            <Setter Property="Foreground" Value="White" />

                            <Setter Property="Background" Value="Transparent" />
                            <Setter Property="SelectionBrush" Value="{StaticResource back}" />
                            <Setter Property="BorderThickness" Value="0" />

                            <Setter Property="HorizontalAlignment" Value="Left" />

                        </Style>

                        <Style TargetType="Button">
                            <Setter Property="BorderThickness" Value="0" />
                            <Setter Property="Background" Value="Transparent" />
                            <Setter Property="Foreground" Value="White" />

                            <Setter Property="FontWeight" Value="Regular" />
                            <Setter Property="FontSize" Value="15" />
                        </Style>

                    </Grid.Resources>

                    <Grid.ColumnDefinitions>
                        <ColumnDefinition Width="25"/>
                        <!--ID-->

                        <ColumnDefinition Width="*"/>
                        <!--Text-->

                        <ColumnDefinition Width="25"/>
                        <!--Splitter-->

                        <ColumnDefinition Width="0.3*"/>
                        <!--Time-->

                        <ColumnDefinition Width="25"/>
                        <!--Done-->

                        <ColumnDefinition Width="25"/>
                        <!--Edit-->

                        <ColumnDefinition Width="25"/>
                        <!--Remove-->

                    </Grid.ColumnDefinitions>

                    <TextBox Text="{Binding ID, UpdateSourceTrigger=PropertyChanged}" />

                    <TextBox Text="{Binding Text, Mode=TwoWay}" HorizontalAlignment="Left" MinWidth="45" Grid.Column="1" Name="text_tb"/>
                    <TextBox Text="{Binding Time, Mode=TwoWay}" HorizontalAlignment="Left" MinWidth="20" MaxWidth="40" Grid.Column="3" Name="time_tb" />

                    <Button Grid.Column="4" Content="✓" Click="OnCompleteBtnClick" />
                    <Button Grid.Column="5" Content="..." Click="OnDetailsBtnClick"/>
                    <Button Grid.Column="6" Content="X" Click="OnDelBtnClick" />

                </Grid>

                <DataTemplate.Triggers>
                    <DataTrigger Binding="{Binding Completed}" Value="True">
                        <Setter TargetName="time_tb" Property="TextDecorations" Value="Strikethrough"/>
                        <Setter TargetName="text_tb" Property="TextDecorations" Value="Strikethrough"/>

                        <Setter TargetName="time_tb" Property="Foreground" Value="Black" />
                        <Setter TargetName="text_tb" Property="Foreground" Value="Black" />
                    </DataTrigger>

                    <DataTrigger Binding="{Binding Completed}" Value="False">
                        <Setter TargetName="time_tb" Property="TextDecorations" Value="None" />
                        <Setter TargetName="text_tb" Property="TextDecorations" Value="None" />

                        <Setter TargetName="time_tb" Property="Foreground" Value="White" />
                        <Setter TargetName="text_tb" Property="Foreground" Value="White" />
                    </DataTrigger>
                </DataTemplate.Triggers>

            </DataTemplate>

        </ListBox.ItemTemplate>
    </ListBox>
    <!--End list-->

</Grid>

Проблема в том, что если просто менять свойство ID, то все хорошо. Но как только начать менять местами элементы массива, то у P перестает отображаться изменение ID (Сам ID меняется).

Без перемещения:

С перемещением:

Как исправить отображение изменений ID?