You were correct about Anders moving out earlier. I looked into the original church books and there is a note saying Anders left already in 1876 without moving attest. Guess he was "signed out" when rest of his family moved 1880.
At the subscription site svar.se the passenger lists are scanned and when looking through the lists for 1876 I found Anders Hansson with contract no 106 from Halmstad, age 33,going to NY. The ship was ångfartyg Rollo from Gothenburg to Hull April 14th.