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Neither the parents or the child are Canadian citizens.

Yes. Depending on the circumstances.

If the parent who submitted the application has sole legal custody of the child, then they can apply without the consent of the other parent.
 
Yes. Depending on the circumstances.

If the parent who submitted the application has sole legal custody of the child, then they can apply without the consent of the other parent.

Thank you for your response!

In this case both parents have being residents in Canada for 2 years and have equal custody of the child... and they are all living in Canada at the moment with Work Permits that expire in March 2021. The husband wants to return to their home country and the wife wants a divorce and wants to stay in Canada, so the mother wants to extend the child's permit or even apply for permanent residence to keep the child in Canada. In this case the father has been the primary caregiver of the child for the past 7 years.

Thank you for your response in advance!
 
Thank you for your response!

In this case both parents have being residents in Canada for 2 years and have equal custody of the child... and they are all living in Canada at the moment with Work Permits that expire in March 2021. The husband wants to return to their home country and the wife wants a divorce and wants to stay in Canada, so the mother wants to extend the child's permit or even apply for permanent residence to keep the child in Canada. In this case the father has been the primary caregiver of the child for the past 7 years.

Thank you for your response in advance!

This is a complicated situation and they should be working through a family lawyer to resolve this.

Since there is shared custody, permission from the mother would be required in order to remove the child from Canada and take the child back to the home country. The husband cannot remove the child from Canada without the mother's consent. Since the child is already in Canada, I don't believe the father's permission would be required to extend the child's status in Canada since the child is already in Canada.