Different cell advance one month

Hi,

Beginner here. I have a sheet that tracks customer payments. I'm trying to come up with a solution where entering a date in one cell advances a set cell one month. For example, entering the payment date for January will advance the date in the 'Due' cell. Completing the date in the rest of the months affect the same cell. Or, even simpler, just applying a cell style (change the month cell to green) does the same thing. Thanks in advance for your help.

 

Mark