More context is needed to be sure. My first reaction is that "she seems to have been ill" means that from her present condition it looks like that she was recently ill; "it seems that she has been ill" could indicate that she is still ill.
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Anonymous Is it correct to change "she seems to have been ill" into "it seems that she has been ill" rather than "it seems that she was ill"?Yes. In fact I'd consider that a closer paraphrase than the one with 'was'.