By the way, the FP request seems to be the least of your concerns. I'll tell you a story from a kind employee at ServiceOntario. I had shared it here before as well because of the profound impact it had on me.
I went to ServiceOntario to apply for my health-card, but at the time, I only had my landing paper with me. Mind you, this is the landing paper from 2002, so it's quite an artifact. Almost as a rule, I would face issues when presenting my landing paper, appallingly even at ServiceOntario. This time was no different. After arguing with the lady at the counter for a bit, I was finally reassigned to someone more senior and experienced. This employee also interestingly faced similar problems as mine in their own personal life.
Apparently, her husband faced many issues when applying for his citizenship because he did not have his landing paper. I believe he failed the interview and was told to either apply for a replacement COPR or simply look for the original. He resorted to applying for the replacement, which itself was due to take nearly a year to process. However, after a while, they eventually found the landing paper. Still, unfortunately, the interview's whole rescheduling took quite some time - over a year, if I am remembering correctly.
The moral of the story, according to the employee, was that I should keep my landing paper extremely safe, at least till I become a citizen. They said that the landing paper's request was totally out of the blue & ended up being quite costly. You can bet my landing paper is in a fire proof safe as I write this.
Therefore, I would either look for the landing paper or try procuring a replacement, if I were you. I hope it ends up working out, all the best!