It looks like the CFC prefers the original owner to make the transfer. I copied the following from the Firearms Centre Fact Sheet on
Selling, Giving or Trading Firearms:
Telephone Transfers
The telephone process generally provides a quick and easy way to transfer and register a firearm to a new owner. To apply by phone, call 1 800 731-4000 and select the transfer option from the menu of services. Please have the following information handy when you call:
your full name, address and firearms licence number;
the name, address and firearms licence number of the new owner; and
the registration certificate number and firearms identification number of the firearm, as indicated on the registration certificate.
The transfer agent will guide you through the process.
You can let the new owner have the firearm as soon as you have been notified that a new registration certificate has been issued. The new owner will receive the new registration certificate in the mail, usually within a few weeks.
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