Seeking an advice on how to handle PayPal Chargeback

hello warriors,

So, I have been PayPal user for a very long time. I am not new to disputes or chargbacks.

However, today I am interfacing with an interesting unique situation.

I have client who hired us to work for him on SEO project, we done the work for a month and half ( he is paying for hour times per hour ). He then stopped working with us and opened a dispute. on good faith, I emailed him and reach to a partial refund agreement which we did and he accepted on PayPal. Everything seemed fine. Until today when he opened 2 claims this time through his credit card issuer which do over writer PayPal power ( I wasn't even aware you can open 2 dispute for the same transaction until today). PayPal already refunded him partially, but now the credit card claims these are not authorized charges. I have sufficient proof from ( emails, screen shot of work done, reports, and other proof that he is the same person and that the work is done as promised ). In addition to the PayPal original case which he accepted through PayPal.

My experience it is hard to win a chargeback, if he won the charge backs. He will get 1.5 month of one of my employees salary + the partial refund equal have and I will have to deal with PayPal fees for the chargeback.

Does anyone have an experience on how to deal with such a situation. I provided PayPal with all evidence, emails, and even case no, and screen shots, as well as report showing all of our work. I personally wouldn't be concern with a dispute because he got no basis, but a claim of unauthorized transaction, we know how that usually goes

Is there anything else I am missing, it is pretty terrible to have such a client. He is right no holding more money that what he originally paid us.