I know that maintaining the PR status while living abroad is possible in two cases: when accompanying a Canadian citizen who is their spouse, and when employed on a full-time basis by a Canadian business or in the public service of Canada or of a province.
My husband, sponsored by me, landed in Canada on March 2011. He then left Canada 1 week later, without even getting his PR card, which was couriered to him later by someone. Now, all our marriage turned out to be fraud. He had no intentions to live neither with me nor even in Canada. All he needs is Canadian passport. Now he is trying to “make a friendship” with some people who are working at Immigration office in Canadian government, hoping that they will help him to get a Canadian citizenship.

My question is: Is it possible to apply for citizenship while living abroad under one of circumstances mentioned above? Let’s assume, these “officials” will manage to arrange for my husband a “full-time employment with Canadian business or in the public service of Canada abroad”. Will he be able to apply for citizenship in 3 years?
Or one has to physically live in Canada for 3 years out of 4 to be eligible to apply for citizenship?
How can I fight all this crime?

Call CIC and chat with them.

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Dimple2001

Fraud marriages are being taken seriously by the authorities now a days.

Since you said your marriage was a fraud, before talking to CIC be clear that you are safe and immune from any penalties as a sponsor. Your act of vendetta should not go against you.

Just a bystander comment. Feel free to ignore it.

Like Dimple said ... if you want to STOP the crime and create trouble to your then husband, write to CIC. But as san-hugo suggested .... your safety is important whatever you do. You can be in trouble if you are a party to the fraud.