Basic question is: Can her marital status still be changed from single to common law.
You say 'partner', not 'girlfriend'. So were you two living together before she went to Canada? If you two lived together for a year before she 'landed' in Canada, but she declared she was single, then she cannot now change that and say you two were common law and try to sponsor you.
If you hadn't lived together for a year before she came to Canada, then you two can either get married and she can sponsor you as her spouse; or you can go to Canada as a visitor, live together for a year, and then have her sponsor you as her common-law partner.