Thanks ChrisA330!

Do you have also an idea why it wasn't possible for the agent at the check-in counter in LIM to check me in and issue the last boarding pass? Alternatively, it was not possible for me as well to do it online (the error message: "Partially checked-in. We was unable to check you in to all of your flights. Please see an agent at the airport for assistance"

Online the gate agent in PUJ was able to do it (and this agent have not asked me for any documents)

It's strange because in 2019, I made BCN-YUL-BOS then BOS-ZRH-BCN, and I got all my boarding pass on the first entry point (BCN then BOS)