If a person makes up a presumed missed Dhuhr prayer during the time of the current Dhuhr, and it turns out no makeup prayer was due, does it count for the current Dhuhr?

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Two opinions exist on whether a prayer performed while believing one owes a makeup Dhuhr, but subsequently found to be free of obligation, counts for the current Dhuhr. One view holds that it counts because the prayer intended was specific, and the error was only in the timing (Waqt), which does not invalidate the specific prayer, similar to when one intends a makeup prayer for yesterday but had another makeup prayer from the day before. The second view states it does not count because the person did not intend the specific current prayer, paralleling one who intends to make up Asr but it counts for Dhuhr.