Binding from a UserControl property to its view model not working

Question

I've this simplified case:

• MainWindow shows a TextBox and a UserControl.
• The UserControl has a dependency property to receive the TextBox text (bound in window XAML)
• The received text is bound to a view-model property in UserControl code-behind.
• The view-model converts the input text into camel case.
• Camel case text is displayed using a TextBlock in UserControl.

I can see the user control receives the correct value of the TextBox, however this value doesn't reach the view-model, I can't understand why.

MainWindow

Window x:Class="WpfApp5.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    xmlns:local="clr-namespace:WpfApp5"
    mc:Ignorable="d"
    Title="MainWindow" Height="450" Width="800">

    <StackPanel>
        <Label Content="Original:"/>
        <TextBox x:Name="tb"/>
        <local:CamelStringBox OriginalText="{Binding ElementName=tb, Path=Text, Mode=OneWay, UpdateSourceTrigger=PropertyChanged}"/>
    </StackPanel>
</Window>

Code-behind:

using System.Windows;

namespace WpfApp5 {
    public partial class MainWindow : Window {
        public MainWindow () {
            InitializeComponent ();
        }
    }
}

UserControl CamelStringBox

<UserControl 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" 
         mc:Ignorable="d" 
         
         x:Class="WpfApp5.CamelStringBox"
         xmlns:local="clr-namespace:WpfApp5">

    <UserControl.DataContext>
        <local:CamelStringBoxViewModel x:Name="vm"/>
    </UserControl.DataContext>

    <StackPanel>
        <Label Content="Camelized String:"/>
        <TextBlock Text="{Binding ElementName=vm, Path=CamelizedText}"/>
    </StackPanel>
</UserControl>

Code-behind:

using System.ComponentModel;
using System.Diagnostics;
using System.Runtime.CompilerServices;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;

namespace WpfApp5 {

    public partial class CamelStringBox : UserControl {

        public string OriginalText {
            get { return (string) GetValue (OriginalTextProperty); }
            set { SetValue (OriginalTextProperty, value); }
        }

        public static readonly DependencyProperty OriginalTextProperty =
            DependencyProperty.Register (
                "OriginalText", typeof (string), 
                typeof (CamelStringBox), 
                new PropertyMetadata (
                    (d,e) => Debug.WriteLine ($"Value received by UserControl: {e.NewValue}")));

        public CamelStringBox () {
            InitializeComponent ();

            // Bind user control OriginalText to view-model Text (doesn't work)
            if (DataContext == null) Debug.WriteLine ($"{GetType ()}: DataContext is null");
            else SetBinding (OriginalTextProperty, new Binding {
                Path = new PropertyPath (nameof (CamelStringBoxViewModel.Text)),
                Mode = BindingMode.TwoWay
            });
        }
    }

    public class CamelStringBoxViewModel : ChangeNotifier {
        private string text;
        private string camelizedText;

        public string Text {
            get => text;
            set {
                text = value;
                RaisePropertyChanged ();
            }
        }

        public string CamelizedText {
            get => camelizedText;
            private set {
                camelizedText = value;
                RaisePropertyChanged ();
            }
        }

        // Never triggered
        private void OnPropertyChanged (object sender, PropertyChangedEventArgs e) {
            if (e.PropertyName == nameof (Text)) CamelizedText = Camelize (Text);
        }

        private string Camelize (string text) {
            if (text == null || text.Length == 0) return null;
            string[] s = text.ToLower ().Split (' ');
            for (int i = 0; i < s.Length; i++) s[i] = char.ToUpper (s[i][0]) + s[i].Substring (1);
            return string.Join (" ", s);
        }
    }

    public class ChangeNotifier : INotifyPropertyChanged {
        public event PropertyChangedEventHandler PropertyChanged;
        public void RaisePropertyChanged ([CallerMemberName] string propertyName = null) {
            PropertyChanged?.Invoke (this, new PropertyChangedEventArgs (propertyName));
        }
    }
}