I propose that the following two Henrys are the same person. Below is a summary of the records that I have found. Any discrepancies are easily explained away. A curious complication is Anna Kolthammer - was her husband an unidentified Kolthammer or this man, who left her to head west? It sure seems like it was Henry since both were in Manhattan, New York. The only other Kolthammer to arrive in America before 1900 was John who immigrated in 1883 with his wife and daughter. They went to Wisconsin, which had a large German population, then to Colorado. John is very likely Henry's brother.
Christoph Heinrich (Henry)
August 1880, immigrated
Nov 1880, declaration of intention to naturalize as US citizen
1886 October, naturalized, cigar maker
1886 NYC directory, segarmaker
1887 NYC directory, segarmaker
1887 NYC directory, segarmaker, at another address (I wonder if this was really 1888)
1889 NYC directory, sigarmaker
(all the addresses were in Manhattan)
no records that include his age
Heinrich Christoph (Henry) born 1849
1882 immigrated (according to 1900 census)
c1883 married Katherine Hamm (where?) (date according to 1900 census)
1887 applied for homestead in Colorado at the same time as a Johann Kolthammer
1889 son born in Seattle, Washington, USA
1890 in Seattle directory, cigar maker
1890 relinquished Colorado land 1891 in census in British Columbia, Canada
1900 in census in Seattle, cigar maker,naturalized
1911 in census in British Columbia, cigar maker
1928 wife died
1936 died in Vancouver, BC son Harry remained in the Vancouver area
1880 September passenger list to NY, with children Bernhard and Augusta
1900 census, Manhattan, NY, widow, with children, son Bernhard a cigar maker
1902 died, NY, of appendicitis, maiden name Moeller