Whether it's a current customer or a prospect, congratulating him or her on a new job will keep you in mind when they are looking for a vendor. It's a gracious gesture and shows that you are on top of what's going on in that company.
1234, Main Street
Boston, MA 02123
<Recipient Address Goes Here>
Congratulations on your new position at <name of customer's company>. They have always hired great people. I'm sure you will be as successful in your new position as you have been in the past.
New jobs are always a challenge and if there is any way I can help, please don't hesitate to call. Best of luck with your new responsibilities.
encl: <List of enclosed items goes here>