His baptism transcription:

First name(s)           Henry James
Last name               Trotter
Birth year              1800
Birth date              26 Jan 1800
Baptism year            1800
Baptism date            26 Feb 1800
Father's first name(s)  John
Mother's first name(s)  Jane Sophia
Parish                  St George, Hanover Square
County                  Middlesex
Country                 England
Page                    382
Archive                 City of Westminster Archives Centre
Record set              Westminster Baptisms
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His very likely Death Duty record:

Record set                   Index To Death Duty Registers 1796-1903
First name(s)                Henry James
Last name                    Trotter
Death year                   1827
County                       Sussex
Court                        Canterbury Prerogative Court
Residence                    HASTINGS
National Archives reference  IR27/36
Category                     Birth, Marriage, Death & Parish Records
Subcategory                  Wills & probate

I have downloaded the 1827 index from TNA and it shows:

March 1827: two entries for Robert Trotter as administrator, indexed to Vol 1, folio 154
The intestate persons were: John Trotter and Henry James Trotter

I can reasonably speculate that Robert, the eldest son, was administering the estates for his father and his brother, both having died at much the same time.
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