A few changes:
You are using a listbox for the first Name, but there can only be one person for a specific duty for a specific week, so I changed it to a textbox.
I changed the names of your listboxes and textbox so when reading the code you can tell what they are (e.g., ListBox1 is now listboxDuty).
I replaced your checkbox with a button to make the replacement. IMHO this is a better user interface design, unless you want them to be able to go back and forth, checking and unchecking the box. That didn't seem likely but if so, let me know.
I added a Close button.
Edit: I didn't preview before posting and I see that some conversation has happened since I started. I did not address your duplicate problem. Will revisit that as time permits now that the issue is a bit clearer.
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