Hans Olsen born 1850 in Norway

I am searching for descedant of Hans Olsen who emigrated to New Zealand somewhere in the 1870's. He a brother of my greatgandmother was born in the District Borre/Nykirke in Vestfold, Norway 15/7-1850, and he was confirmated in Borre 11/6-1865. After he emigrated all trace of him has been lost.. Found a letter he wrote to his sister, my greatgrandmother is marked Okura 15 nov. 1890. In the letter he wrote that he left Norway in 1870 and went from Kragerø, Norway to UK.. He saild some trips to USA, then he saild to New Zealand from UK. Before 1890 he bougth land 12 miles from Auckland and lives 2,8 miles from the hot springs. He contacted to Railway Company to sell timber, I the letter he is still bachelor, this is in 1890 so he must get married after this. He did it well and sent money to his family back .in Norway, Any information is more than welcome!