Passage from Europe to Cuba then New York?

I have the exact date of departure for a Danish emigrant but do not have the name of the ship because the Danish Emigrant Database does not give the name of the ship if one take a feeder ship first. This emigrant has been found arriving on 19 May 1880 on the Saratoga into the NY port from Havana, Cuba, along with another 11 Danish and several other European immigrants Does anyone know about this type of migration and which ports in Europe and ships went to Havana? Thanks. Jon