Hello...
Can't help with the passenger list (sorry) but do you know the names of Anna Marie's parents i.e your g-g-g-grandparents.
Anne Margareth was born in 1851
Anna Maria was approx born in 1857
FamilySearch have a Hans Christian MADSEN and his wife Kirstine Maria CHRISTENDATTER living in Brondum, Ribe, Denmark. Amongst their children are two daughters, Anna Magrethe MADSEN b.1851 and Anna Maria MADSEN b.1857.
Possibly you already know this. If not, from where did you get the dates that you mentioned in reply #7.
Anna Magrethe MADSEN b.1851https://familysearch.org/ark:/61903/1:1:XYZX-WJ3Anna Maria MADSEN b.1857https://familysearch.org/ark:/61903/1:1:XYZX-WPPVarious family members, including Anna Maria, are still in Brondum in the 1860 and 1870 censuses.
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Do you have a copy of the 1881 PREBENSEN/MADSEN marriage certificate mentioned by Janette in reply #6 as it should mention the bride's parents.
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It's possible that Anna Magrethe's husband Hans KROSP came to NZ earlier with his parents Jacob and Anna. Maybe mid to late 1860's.
http://tinyurl.com/kcftez2Having said that, just because his parents supposedly migrated to NZ there's no reason their twenty-ish year old son Hans would have travelled with them.
For what it's worth, Hans' older brother is still in Denmark/Prussia in 1868.
https://familysearch.org/ark:/61903/1:1:FV5V-15S---
And if you've not seen it here is Anna Magrethe's Will...
http://tinyurl.com/qzqe29fRegards
Beg