public partial class Form2 : Form
{
    public string TextBoxValue
    {
        get { return textBox1.Text; }
        set { textBox1.Text = value; }
    }

    public void SetTextBoxValue(string value)
    {
        textBox1.Text = value;
    }
}

public partial class Form1 : Form
{
    private Form2 _form2;

    public Form1()
    {
        InitializeComponent();
        _form2 = new Form2();
        _form2.Show();
    }

    private void button1_Click(object sender, EventArgs e)
    {
        _form2.SetTextBoxValue("Hello from Form1!");
    }
}