| Writing "Paid in full" on a check is called a restrictive endorsement, and also referred to as "accord and satisfaction." It is not accepted in every state, and in the ones where it is legal, there may be some specific rules that must be followed before it will hold up.
In California a letter must be written in advance explaining the situation and that a check will be sent for less than the total due. Then the check can be sent, and if cashed may hold up in court. In other states there are restrictions on where it can be sent, such as not being allowed to be sent to a PO or drop box. Sometimes there has to be a legitimate dispute before the lesser amount will be accepted.
The first step is to determine if your state allows this practice, and second to determine if all the rules were followed properly. In most cases the rules are outlined in the UCC under Chapter 3 - Negotiable Instruments - Restrictive Endorsements. | 
