At http://www.ellisisland.org/http://www.ellisisland.org/ there is an entry in 1909 for a Charles M. Bonnett, aged "10 years 3 months", from Trinidad.
On the actual image, it looks to me like he's aged 19 years 3 months. His relative at home is "Mrs Bonnett", 60 Rosalind, Woodbrook, Trinidad. He is headed for Alabama (town name Tusher?) and is an engineer.His contact in the US is the "Tushigee Institute" in Alabama.
http://www.collectionscanada.gc.ca/databases/cef/001042-100.01-e.phphttp://www.collectionscanada.gc.ca/databases/cef/001042-100.01-e.php - his attestation records can be seen here. He's listed as "Charles Monton Bonnett" Gives an exact birthdate - 9th January 1892, at Port of Spain, Trinidad. Shows he was living in Detroit when he signed up, and had a cousin, Dr Robert Harris Brooks, in Rome, Georgia.
You could write to them for his full military records, which might give some info about where he went to directly after the war.
There's a Robert Brooks b. 1882 West Indies in the 1920 US census in Georgia.Also a Marie Brooks was travelling with Charles when he came to the US - heading to her brother, Dr R. Harris Brooks.