As per the title, I want to "move" the contents of a cell one column to the right once a week, specifically Sunday at 11pm
Must I use a script for that?
This piece of script will move the first entry of a row range to the next column:
I've created an example file for you: Copy and Paste Cell Contents Once a Week
Add the script under Script Editor from the Tools menu. Press the "bug" button to debug the code and to authenticate the script. Goto Resources (in the script editor) and set the trigger as shown.