Normally "imashita" is used in such a case, but in some written things (especially old tales for children) "arimashita" is often used. So, this is not wrong, and I imagine it was used to be used before. But it's not used as the modern language, at least as the spoken one, so the expression like "onnanoko ga arimashita" gives an old-fashioned impression.
I will appreciate your answers. Thanks so much.
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