It is highly likely to be he who is in the 1881 census at a house in London Road at Reigate Foreign, Surrey and as a boarder scholar; if so he was 10 years old and born in Caernarvon, Wales [in fact his birth certificate shows him to have been born in Llandisilio, Anglesea.]  The house was headed by a clergyman, John Gooch MA, who may have been giving tuition to the three boys in the house.
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In the 1891 census he was living at No 3 Rectory Road, Wivenhoe near Harwich, Essex with his father and a housekeeper and housemaid, the latter two being either sisters or mother and daughter.  He was a draughtsman aged 20 and born in Menai Bridge, Anglesea.

In 1891 he was present at his father's death in Wivenhoe, Essex, England.  He was then 20 years old.
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He came to the USA twice, as recorded in Ellis Island: 1894 and again in 1906.
Before the first world war he was working as a civil engineer in Virginia and Tennessee.
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Here's a note to a descendant of his, summarising a day's research:
Date: Thu, 25 Sep 2003 18:20:08 +0100
From: Tim Powys-Lybbe <tim@powys.org>
To: ZZZZZZZ
Subject: Your grandfther...

Today by a happy accident of a failed appointment, I got to the PRO at
Kew and did three studies of AWL:

1. His first military career from 19 Jun 1893 to January 1896, from the
   volumes of the Army List.

2. His second military career from 2 Sept 1914 to 11 or 12 July 1916,
   also from the volumes of the Army List..

3. His military records from the war Office for 1914 to 1916.

Now for the nitty gritty, one by one:

First Military career:
=====================
18 Jun 1893: Was commissioned as 2nd Lieut in the 4th Battalion of the
   Yorkshire regiment.

12 May 1894: Was commissioned at 1st Lieut, still with the 4th
   battalion of the Yorkshire regiment.

31 Dec 1895 still in Yorks regt, but by 31 Jan 1896 he was no longer
   there.

Questions:
(a) Where did he go to school?
(b) What did he do between leaving school at age c. 18 and becoming 1st
Lieut at age 21?   (Might he have been at Sandhurst Military Academy?)
(c) What caused him to resign his commission?

Second Military career
======================
2 Sep 1914: Joined the army in the Royal Fusiliers.

29 Oct 1914: Commissioned

4 Nov 1914: had temporary commission as 1st Lieut in the 10th Battalion
  of The Leicestershire Regiment.

30 Nov 1914: Commissioned as temp Capt, still in the 10th Bn of the
   Leics regt.

1 Jun 1915: Transferred to the 9th Bn of the Leics, Regt, still as a
  Capt.

24 Apr 1916: Commissioned as Major, still in the 9th Bn of the Liecs
   regt.

11-12 July 1916: killed in action.

War Office records
==================
There are 80 odd pages of these and I can get them photocopied by the
PRO at 40 pence a sheet = c. £33 ukp plus postage.

Significant features in the documents, which I was allowed to read
through:

(a) They were principally his joining papers and the rest on the
    administration following death.  No details of what he did at all.

(b) There was some unclarity about the date of his death and the war
    Office finalised on the 12th July.  But it could have been the 11th.

(c) When he enlisted he gave this information:
    address: Slanderwick Court, Frome, Somerset where his aunt
             Constance Selina Trotter (wife - or widow? - of William Sampson
             Trotter) lived.
    Next of kin: W C Trotter at Slanderwick Court, c/o Mrs Trotter
    Wife: Cameron Browning of USA
    Children: the two of them, including young WC.
    Trade or profession: None

    The next of kin and the address of Slanderwick Court led to some
    confusion when he died.

(d) He was 5 ft, 11 in tall, weighed 162 lb, had a chest measurement of
    38 ins which expanded by two ins on breathing in.  He was 43 years
    and 10 months.  This was on 2 Sep 1914.

(e) He left no will, neither in England nor USA.  The army owed him, and
    paid his estate, £147 ukp at death, which the lawyer seemed to have
    declared to be the sum total of his net worth in England.

(f) In his file there were the original letters from three women to the
    war office:
    Cameron Browning Trotter
    Constance S[elina] Trotter
    Julia B Bucknill (Miss) of Epsom, Surrey, who described herself as "a
    very old friend".

More questions:
(i) What was his trade or profession before arriving in England?
(ii) Who had he meant to appoint as his next of kin?
(iii) Why had he not written a will?
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In the TNA Medals archive ref WO/372/20, Image Ref 13615, he was down as awarded the 1915 star, was a Captain then Major in the Leicester Regiment and K in A 12/7/16 (12 Jul 1916).

There is a date of the 11/2/22 which probably means the last entry on the card.
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The CWGC site has:

Name: TROTTER, ALEXANDER WILLIAM LEWIS
Initials: A W L
Nationality: United Kingdom
Rank: Major
Regiment/Service: Leicestershire Regiment
Unit Text: 9th Bn.
Age: 46
Date of Death: 12/07/1916
Additional information: Son of Alexander Kenyon Trotter, of Horton Manor, Epsom, Surrey; husband of Cameron B. Trotter, of University, Virginia, U.S.A.
Casualty Type: Commonwealth War Dead
Grave/Memorial Reference: III. H. 8.
Cemetery: DANTZIG ALLEY BRITISH CEMETERY, MAMETZ
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