It is possible to retrieve the window handle to a message box. Recently there was a thread showing how to get it using FindWindow API function triggered by a timer. The FindWindow uses window caption as an input parameter.

After having this handle you can get device context for the messagebox window and then either copy window's image to the clipboard, or send it to a printer.

Another part of this task seems to me more problem one -- a user interface or in other words how to initiate printing.