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Yes ma'am. There is no law against them calling it his office or actually any law defining what an office is, especially if he works out of his house.
However, his behavior is not only inappropriate but also illegal. As I pointed out in the other question thread, he has clearly broken the law in at least one way and maybe more. It is likely that if he is convicted the judge will not allow him to continue operating out of his house that way. In addition, that specific crime is regarded as a "sex crime" and he will likely have to register as a sex offender which carries a lot of extra penalties.