Dynamicly change TextBox width when column header resizes (WPF)

Question

Ive created templated column in DataGrid with textbox in header template for grid filtering. Is it possible to make dynamic resize of textbox, so that textbox was 100% width of columns width?

<my:DataGrid AutoGenerateColumns="False" Name="dgEmployees" IsReadOnly="True" Background="DarkGray" GridLinesVisibility="All" SelectionChanged="dgEmployees_SelectionChanged" Margin="0,29,0,0">
        <my:DataGrid.Columns>
            <my:DataGridTemplateColumn Width="auto">
                <my:DataGridTemplateColumn.HeaderTemplate>
                    <DataTemplate>
                        <Grid HorizontalAlignment="Stretch">
                            <Grid.RowDefinitions>
                                <RowDefinition Height="20"/>
                                <RowDefinition Height="auto"/>
                            </Grid.RowDefinitions>
                            <TextBlock Text="Фамилия"/>
                            <Border CornerRadius="5" BorderBrush="White" BorderThickness="2" Grid.Row="1" Background="Black" HorizontalAlignment="Stretch" MinWidth="200" Margin="0,0,0,0">
                                <TextBox x:Name="tbFilter" KeyDown="TextBox_KeyDown" BorderBrush="Transparent" Foreground="White" Background="Transparent" Margin="3,0,3,0"/>
                            </Border>
                        </Grid>
                    </DataTemplate>
                </my:DataGridTemplateColumn.HeaderTemplate>
                <my:DataGridTemplateColumn.CellTemplate>
                    <DataTemplate>
                        <TextBlock Text="{Binding Path=FName, Mode=OneWay}"/>
                    </DataTemplate>
                </my:DataGridTemplateColumn.CellTemplate>
            </my:DataGridTemplateColumn>
        </my:DataGrid.Columns>
    </my:DataGrid>