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Unfortunately you can't backdate a CFA in that way - or at least not in the way that's going to help. I presume this took place on assessment of costs, with a order for costs already having been made?
If at the time of the costs order there is a defect in a retainer, such that the paying party actually has no liability to pay, that defect can't be fixed by a retrospective agreement. The retainer cannot be changed to increase the inter partes costs burden on the paying party after the costs order has already been made.