This is a simple letter which clearly states what the payment is for. Specify amount, check number and whether this represents full or partial payment. If it is a partial payment, tell them why.
1234, Main Street
Boston, MA 02123
<Recipient Address Goes Here>
Enclosed is check number <check number> for <$amount of check>. This is <full/partial> payment on invoice number <invoice number>.
<Optional explanation for partial payment.>
encl: <List of enclosed items goes here>