Nothing more found on him, as Charles A Jackson, in earlier or later censuses, nor any death.

But a Charles Arthur Coster Jackson was the first executor for Charles William Coster in 1933.  And this could be a son with this death:

First name(s) CHARLES A C
Last name JACKSON
Gender Male
Birth day -
Birth month -
Birth year 1883
Age 68
Death quarter 3
Death year 1951
District HOVE
County Sussex
Volume 5H
Page 315
Country England
Record set England & Wales deaths 1837-2007
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This led to this 1901 census try showing him with a young second wife who could not have been the mother of his son:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year  Occupation  Birth place

Charles A Jackson Head Married Male 43 1858 Living On Own Means  South America
Lizzie Jackson Wife Married Female 28 1873 -  Brighton, Sussex
Charles A C Jackson Son Single Male 17 1884 - London, Middlesex
Fanny Eastwood Servant Single Female  18  1883  General Servant Domestic  Burwash, Sussex
Annie Avis Servant Single Female 20 1881  Cook Domestic  Rotherfield, Sussex

Ref: RG13 pice 929, Folio 72, p. 9
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There were these possible marriages:

Q3 of 1887 to either Elizabeth Skeate or Elizabeth Sheate in St Pancras, London

Q4 of 1900 to Cornelia Elizabeth Skerratt in Woolstanton, Staffs

I’m inclined to the first, though Lizzie would have been a mere 14 at marriage.
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No sign of him in the 1911 census.

Nor can his death be clearly identified.

Their marriage:

Surname   First name(s)      District   Vol  Page
Marriages Sep 1880   (>99%)
Coster Ellen Georgina H Marylebone 1a 1010
Jackson Charles Alfred    Marylebone 1a 1010
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