If the customer is being moved out of a position where you will do business with them, they still have the power to recommend you to their successor. Aside from being a gracious gesture, it always pays to enhance the customer relationship.
1234, Main Street
Boston, MA 02123
<Recipient Address Goes Here>
Congratulations on your promotion to <customer's new title>. It's always gratifying to see hard work and talent rewarded. I'm sure you will be as successful in your new position as you have been in the past.
Best of luck with your new responsibilities and if we can be of any service, please don't hesitate to call us at <telephone number>.
encl: <List of enclosed items goes here>