It can take quite a lot of time. Certainly many months, even longer.
IRCC has to take the time to review the submission and assess against their records and the records available to them. They they have to make a decision on whether they will pursue the case or not. If they decide to pursue the case, the person against whom the report has been filed is given an opportunity to present their side of the story. IRCC then assesses further to decide if they are going to pursue revoking PR status. If they decide to do that, the person against whom the report was filed then has a chance to appeal (to the best of my knowledge). So not a short process.
Also, the person who filed the report is really not kept up to date on what is happening for privacy reasons. So you basically submit the report and you generally wait a long time without knowing if anything is happening and if IRCC has even decided to pursue the case.
Social media has become a powerful tool for Investigators on a whole.
Some people post anything & everything on social media.
To make your case stronger for IRCC you should check the social media of her friends, family, co-workers etc..
There could be clues, ancient posts, pic, etc. that prove her & this guy knew each other before.
Perhaps they were even a couple before, but were separated by circumstances beyond their control.
Maybe he can't sponsor, and she needed to use someone to sponsor her to re-unite with him.
Again, I don't know what really happened between you & your ex.
Just going what you said.