"in his case" is more natural. "in the case of him" is intelligible but doesn't feel as natural. "In his case, we will not grant permission" most probably means "We will not grant permission to him".
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deepujiDo "In the case of him" and "In his case" both convey that we are trying to refer to that person?There is no difference between the two in this respect. What I said applies to both.
deepujiI mean Can I replace them with say, "with regard to" or "regarding"?In your sentence, these do not work as well as "in his