Have you been exporting the object from Poser with "As Morph Target" checked?

I would try running a head through your import-export process, from Poser to ZBrush back to Poser, without making any vertex alterations in ZBrush.  Just do the import and export part, then load this "blank" morph onto Antonia's head.  If you get the unwanted motion on this morph, too, you can fix all the morphs by setting the "blank" morph to -1.0 and combining that with each of the problem morphs, spawning new copies.

If that doesn't work, I've had some luck cleaning unwanted motion out of Antonia morphs in the past, using a Python script.  Depending on the nature and intensity of the motion, however, that may or may not work well.

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Cage can be an opinionated jerk who posts without thinking.  He apologizes for this.  He's honestly not trying to be a turkeyhead.

Cage had some freebies, compatible with Poser 11 and below.  His Python scripts were saved at archive.org, along with the rest of the Morphography site, where they were hosted.