I believe this Henry is listed, for the first time, in Trow’s NY City directory of 1858/59 as: Shaphoff Henry B jr, police, h 668 Water, certainly it wasn’t his father or his son Henry who was only born about 1835.
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LDS 1880 United States Census and National Index
Census Place: Brooklyn, Kings, New York
Source: FHL Film 1254851 National Archives Film T9-0851 Page 735C
Relation Sex Marr Race Age Birthplace
Henry SHAPHOF Self M M W 51 NY Occ: Ship Caulker Fa: MD Mo: NY
Julie H. SHAPHOF Wife F M W 50 DENMARK Occ: Keeping House Fa: DEN Mo: DEN
Charles A. SHAPHOF Son M S W 19 NY Occ: Works In Oil Works Fa: NY Mo: DEN
Therese A. SHAPHOF Dau F S W 17 NY Occ: Vest Maker Fa: NY Mo: DEN
Ida F. SHAPHOF Dau F S W 14 NY Occ: At School Fa: NY Mo: DEN
Jennie E. SHAPHOF Dau F S W 9 NY Occ: At School Fa: NY Mo: DEN
Hattie SHAPHOF Dau F S W 6 NY Fa: NY Mo: DEN
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The 1990 US Census of the United States burned so we lose track of Henry, Julia and there children for 20 years.

The following are City Directory listings except where noted otherwise:
1859 Shaphoff Henry B. jr police 668 Water
1870 Shaphoff Henry B. jr caulker, Eckford n Meserole
He is listed in 1877 (in the directory) and in all subsequent listings as a ship’s caulker
He and Julia seem to provide a very stable environment for the children living at the same address at 70 Newell St. for many years.
1877 Shaphoff Henry B. jr caulker, 71 Newell (Jr)
1878 Shaphoff Henry B. jr caulker, 71 Newell (Jr)
1879 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
1880 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
1880 Census indicated Henry was out of work for 6 months of the census year.86
1881 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
1882 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
1883 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
1886 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
1888 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
Listed in one 1888 & 89 dir as Shapholl
1889 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
1891 Shaphoff Henry B. jr caulker, 70 Newell (Jr)
1892 Shaphoff Henry B. jr caulker, 71 N.J. av
1893 Shaphoff Henry B. jr caulker, 71 N.J. av
1894 Shaphoff Henry B. jr caulker, 71 N.J. av
1895 Shaphoff Henry B. jr caulker, 120 N. J. av
In 1896/97, when Henry is about 60 years old, his address changes to: 183 Ashford.
1896 Shaphoff Henry B. jr caulker, 183 Ashford
1897 Shaphoff Henry B. jr caulker, 183 Ashford
1898 Shaphoff Henry B. jr caulker, 183 Ashford
1899 Shaphoff Henry B. jr caulker, 183 Ashford
1900 Shaphoff Henry B. jr caulker, 183 Ashford
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1900 Census:
Henry is 72 years old and iving in Webbs Academy and Home for Ship Builders at Sedgurik (Sedwick)? Ave. It is an old age home. He’s listed as an inmate and under occupation is stated “no occupation.” Julia is living with a married daughter now Mrs Vollers and claims widowhood as her marital status. The other younger daughter Theresa, age 37 is boarding with other families.
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Henry’s Death Certificate from the City of New York, No. of Certificate: 1107
Henry Shaphoff died at Webb. His parents information is listed as unknown. They stated his occupation as Shipbuilder. He is listed as 73 y 1mo 4 dys. That makes his birth date from the 1900 Census a year off. So he was either born in 1829 or the math is incorrect. I’m betting the math is wrong but we will probably never know.
The Funeral Director was G. W. Howie on Fordham, the best I can read it.
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Just in case:
A “Caulker” filled up cracks (in ships or windows) or seams to make them watertight by using tar or oakum-hemp fiber produced by taking old ropes apart.