Payment of Medicare recouped claim\money

I have a general question. We submitted claims of a skilled Nursing home claims 32 as facility (it should be 31), Medicare paid the claim, but later on they found the facility must be 31 and recouped the money against another patient. We submitted the appeal and Medicare accepted in our favor. Now, the question is after the appeal is accepted, whether Medicare pays that patient claim\money or not.

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We tried half dozens of times to get this answer, whether Medicare pays the recouped money after the appeal is accepted or not; could not find the answer from any of the reps. Wondering any other billing gurus have experienced this situation and what was the course of action, and the outcome? Any feed back will be helpful.

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