Shifting ROW_num when the first entry and the original entry are unequal

Imagine there is an original string and an initial string there is also a 2nd position string a 3rd position string and so on.

I want to make a case statement that the initial string = original string.

case when original string != initial string 

I need original to be initial to be 2nd and 2nd to be 3rd

Does anybody have any ideas?