Trying to trace my German/Samoan connection

My great aunt (85) said her Grandfather Telea Tuala was part German and the only details, London Missionary Society and Moata'a. She was also told that her father Telea had a brother Kornelio who was buried in Moata'a Samoa. I googled missionaries from that time period who came to Samoa and Karl Wilhelm Edward Schmidt comes up working for the London Missionary Society. Karl married a Samoan woman Salaneta who he had a son. Anyone know how I can trace a birth certificate for Karl Schmidt son to see his name or any connection to Kornelio.

Apparently Karl Schmidt married Salaneta in 1857 in Samoa. There are no Governmental registrations from that time, as there was no government of Samoa then. There could be mention of the marriage in the London Missionary Society records, which are held in England, but the copies on microfilm in other places.
I see you are in Auckland, The University of Auckland holds copies of the LMS films in the Special collections of the University Library