[c#] Send Message in C#

You are almost there. (note change in the return value of FindWindow declaration). I'd recommend using RegisterWindowMessage in this case so you don't have to worry about the ins and outs of WM_USER.

[DllImport("user32.dll")]    
public static extern IntPtr FindWindow(string lpClassName, String lpWindowName);    
[DllImport("user32.dll")]    
public static extern int SendMessage(IntPtr hWnd, int wMsg, IntPtr wParam, IntPtr lParam);    
[DllImport("user32.dll", SetLastError=true, CharSet=CharSet.Auto)]
static extern uint RegisterWindowMessage(string lpString);

public void button1_Click(object sender, EventArgs e)   
{        
     // this would likely go in a constructor because you only need to call it 
     // once per process to get the id - multiple calls in the same instance 
     // of a windows session return the same value for a given string
     uint id = RegisterWindowMessage("MyUniqueMessageIdentifier");
     IntPtr WindowToFind = FindWindow(null, "Form1");    
     Debug.Assert(WindowToFind != IntPtr.Zero);
     SendMessage(WindowToFind, id, IntPtr.Zero, IntPtr.Zero);
}

And then in your Form1 class:

class Form1 : Form
{
    [DllImport("user32.dll", SetLastError=true, CharSet=CharSet.Auto)]
    static extern uint RegisterWindowMessage(string lpString);

    private uint _messageId = RegisterWindowMessage("MyUniqueMessageIdentifier");

    protected override void WndProc(ref Message m)
    {
       if (m.Msg == _messageId)
       {
           // do stuff

       }
       base.WndProc(ref m);
    }
}

Bear in mind I haven't compiled any of the above so some tweaking may be necessary. Also bear in mind that other answers warning you away from SendMessage are spot on. It's not the preferred way of inter module communication nowadays and genrally speaking overriding the WndProc and using SendMessage/PostMessage implies a good understanding of how the Win32 message infrastructure works.

But if you want/need to go this route I think the above will get you going in the right direction.