If you got your ecopr, you are a PR already, you are good and safe. You don't need to inform IRCC and your partner cannot do anything about it.
I agree with this overall BUT:
-the partner can inform IRCC - and it has happened (in real life) that unhappy partners can make untrue allegations about what happened and when.
-the real background is that you (
@mbilli) have PR status in your own right and that would be reviewable only if eg the relationship was truly fraudulent (with proof of such) and/or ended before you became a PR.
-IRCC can investigate allegations of so-called relationship fraud - and can take action where those allegations are well-founded and some kind of evidence exists.
-Important: this is done entirely separately from your former partner. If you are not involved anymore, they do not have any rights with respect to your immigration status in Canada (repeat, vis a vis immigration, civil rights are a different matter, eg if you owe each other money or have children or whatever).
-Any financial or other arrangements (eg sponsorship guarantees, which I don't think apply in your case) between your partner and IRCC are unchanged.
-IRCC really does NOT want to be involved with or police 'relationship disagreements.' If they believe it's just a routine relationship break-up ( a "he said/she said"), they'll drop it.
I write this to be clear and to comfort you, not to scare you. The likelihood of IRCC investigating and doing anything is low, even very low (assuming as above that what you've related is truthful). Your partner cannot threaten your immigration status and reporting you to IRCC should have zero effect - just tell them 'go ahead.'
There are some basic steps you can take though to protect yourself: retain any documentation you have or records of the date of break-up and when you stopped cohabitating. If you do not have documentation, write emails and speak to (trustworthy) friends or acquaintances and inform. Keep copies of those and try to have eg your friends note the date of the conversation. If you make any financial or other arrangements to sever ties (getting your name taken off the lease or utiltiies etc), keep records of the date.
If IRCC ever asks any questions of you about this, your existing records and any contemporaneous (i.e. now, from the time of breakup) records or corroboration will add to credibility on the point that the breakup occurred after you became a PR.