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Dear Mr. Moberg,
Thank you for posting your request on History Hub!
We searched Ancestry and located in the Hamburg Passenger Lists (1850-1934) a Jan Hakanson with a wife named Cath.r and children, Johan and August. Here is another reference to that departure from a collection of Swedish emigration records for Jan Håkanson.
We could not find an arrival in New York passenger listing using a surname search or looking for the vessel Grimsby entering the port in June 1866, which would be the likely arrival month. It may be worthwhile to browse each page of the lists for ships that arrived in early-mid June at New York since it is possible that there could be a poor name transcription or spelling that prevents them from appearing in name search results. Please keep in mind that not every list from every ship survived. Although there are many lists available, it is not a comprehensive collection.
Ancestry may charge a fee for using this service. To view this online service for free via ALIC, please come to one of NARA's facilities. For the nearest NARA location, please consult our web page at https://www.archives.gov/locations/. Also, some of the images from Ancestry are available for free on Family Search at https://www.familysearch.org/en/.
We hope this is helpful. Best of luck with your family research!
[Information provided by Elizabeth Burnes, Subject Matter Expert]