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You definitely have an argument that the debt was fully and finally cancelled upon the cashing of your last check with the statement of "Full and Final Payment" in the MEMO space. The better practice is to have a letter accompanying the check specifically stating this is your full payment, and that cashing the check is an acknowledgment of settling the debt.
The cases are sketchy on what is required, and much depends on whether you're dealing with a sophisticated party on the other side. Because you were paying a law firm, it should know the danger of cashing a check with that language on it. Therefore, I think you have a valid defense.