I just did a quick search on the passenger records..
There are 4 Charles Parkers coming to Canada from Liverpool, England.
1901, 1911, 1913 and 1926.
Name: Charles Parker
Gender: Male
Age: 20
Estimated birth year: 1881
Date of Arrival: 17 Dec 1901
Vessel: Corinthian
Port of Arrival: Halifax, Nova Scotia
Port of Departure: Liverpool, England
Occupation: Clerk
Name: Charles H Parker
Gender: Male
Age: 27
Estimated birth year: 1884
Date of Arrival: 25 Jun 1911
Vessel: Teutonic
Port of Arrival: Quebec
Port of Departure: Liverpool, England
Occupation: Farmer
Name: Charles Parker
Gender: Male
Age: 32
Estimated birth year: 1881
Date of Arrival: 9 Jun 1913
Vessel: Corsican
Occupation: Rubber Trade
Name: Charles Parker
Gender: Male
Age: 45
Estimated birth year: 1881
Birth Country: England
Date of Arrival: 17 Jan 1926
Vessel: Montnairn
Occupation: Engineer
(been in Canada 1913-1916) in Montreal