I do not mind. We are just trying to survive paying bilss , mortgage and etc suppor eachother. Sexuality is not important. Eveybody has different preferences and point of views.
So you are saying that you two share bills, mortgage and support each other as friends...
Because common law relationship doesn't mean that. It has to be a marriage like relationship which in most cases involve sexual relationship.
I think this sounds like you are just trying to use the living situation to apply for common law. I don't think this will work since he applied and got his PR as being gay. And your living situation was the same since 2016. As he didn't (and likely cannot) added you as a common law partner back then before he got his PR, you cannot be sponsored by him forever.
As others have commented, he may risk loosing his own PR because of misrepresentation.