Hi Again Alain,
I wanted to let you know about a small correction I've made to the above post. You do not need to have an X Server running for this type of Debug Configuration - the user interface for your program will display in the Linux session where you've started the program, just as it did with cobanimsrv. Also, you don't need to enter anything in the "X Server (DISPLAY)" field on the Run Configuration dialog.
Please let us know how it goes when you try out cross-session debugging in Visual COBOL for Eclipse.