There are a couple of ways you can do this:
1) You could use the actual windows clipboard: Clipboard.GetText
] and Clipboard.SetText
] are the easiest way to do it.
2) You could create a class level string variable to hold the information. This is pretty easy, just copy the text in and out. Use this way if you don't want to disturb the actual clipboard content for other applications.
Either way, you just need to read the data out using the TextBox.SelectedText property and either set it it in the other TB, or set the TextBox.Text property if you want it to replace all the text.