The Canadian prime minister is responsible for providing recommendations to Her Majesty the Queen for the appointment of the Governor General of Canada.
The Prime Minister, usually with the Attorney-General pick a Governor-General and then tell the queen to nominate that person to the office.
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The Governor General is a person suggested by the prime minister to be the King or Queen's representative in that country
How is the governor general
Which governor-general? The governor-general of Canada is in a different position than the governor-general of Australia.
The Governor General (or "Governor-General", in some realms of the Commonwealth) represents Her Majesty the Queen. The Governor General appoints the person best able to command a majority of voices in the Lower House to act as prime minister. The Governor General also summons, prorogues and dissolves Parliament, and reads the throne speech at the opening of each session of the legislature. The Governor General also grants royal assent to bills (as the Queen's representative) before they can become law.
The Governor General is David Lloyd Johnston.
The Governor General of Jamaica is addressed directly as 'Your Excellency' and indirectly as 'His Excellency the Governor General'
As per the Office of the Secretary to the Governor General of Canada, Canada does not use a hyphen for "Governor General".
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Elliot Belgrave is the Governor General for Barbados.
Arthur Foulkes is the Governor General for the Bahamas.