Briefly, if you cash a check for less than the amount owed to you and that check has “paid in full” written on it, you do not necessarily lose your right to the rest of your owed money. Several factors come into play. For example, do the facts of your case demonstrate that you and the other party disagree about the amount owed? If the answer is yes, and you cash a check for less than the amount owed to you, then you may have extinguished your legal right to the rest of your money, even if the check does not have conditional language such as paid in full written on it.
To the contrary, if no dispute exists, then cashing a check that is for less than the amount owed to you may not extinguish your legal right to the rest of your money, even if the check has conditional language such as paid in full written on it.
As said, the situation can be complex and involves much more than the above-mentioned scenarios. The facts of your case as applied to Georgia law will determine the claims you have against the other party.