Embedding a winform within a winform (c#)

Not directly. You can create a usercontrol, move all of the code from your form to the usercontrol and use this in both forms. You might need to change some of the code from your form but probably not much.

Disclaimer

This will work as I am using it in my application extensively. That being said I would pursue the User Control route as depending on how far you carry the embedding things start to flake out. FYI

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Yes this is possible. This is how:

public static void ShowFormInContainerControl(Control ctl, Form frm)
{
    frm.TopLevel = false;
    frm.FormBorderStyle = FormBorderStyle.None;
    frm.Dock = DockStyle.Fill;
    frm.Visible = true;
    ctl.Controls.Add(frm);
}

I have that in a Class Library and then I call it like so from the FORM I want to embed.

public FrmCaseNotes FrmCaseNotes;
FrmCaseNotes = new FrmCaseNotes();
WinFormCustomHandling.ShowFormInContainerControl(tpgCaseNotes, FrmCaseNotes);

Where tpgCaseNotes is the control I want Form FrmCaseNotes embedded in.
In this case a tab page on the Form I am calling from.