Legal Question in Business Law in California

I would say no, unless you expressly made acceptance of the part payment an acceptance of the entire payment plan. My opinion is based on a reading of the statutes forming California's law on "accord and satisfaction," Civil Code sections 1521 through 1526, which includes the payment-in-full check law (section 1526). It seems pretty clear that the intent of the law is to treat an existing obligation as not modified or extinguished by a substitution of another promise or obligation unless the acceptance of the bait is expressly and clearly labeled as acceptance of the entire plan.by the creditor. The same reasoning would apply to "novation" which is discussed in sections 1530 - 1533 of the Civil Code, although I think in your case you have offered and accord and satisfaction rather than a novation.

I don't read your question as concerning whether the check constitutes payment in full, but rather it seems as whether he is accepting the terms in your certified letter, explaining your calculation of the amount due, and payment terms.

Unlike an account stated, which would become binding on the debtor once it had not been disputed, I do not see that your terms become binding simply because you have sent him a certified letter. You would actually have to strike an agreement, which is termed a novation, that he would sign to make it binding.