Hello Yann,
First you need to think through the ethical aspects of this in your context. Messages may contain information of a third party that the parent would see. For this reason it is probably reasonable that there is not an easy way to see another user's messages in the interface. Even for an admin you have to log in as the user to see a users messaging. The student could obviously login in and show messages to the parent, but that may not be sufficient.
Messaging is however included in the Moodle data privacy system. So an admin, privacy officer or student could request a data export and download it. The file content can be browsed to see the exported messages for the user. The capability tool/dataprivacy:makedatarequestsforchildren can be given to a parent role, and the capaiblity tool/dataprivacy:downloadallrequests can also be assigned in the user context so it should also be able to be assigned for the parent role. If so the parent would be able to download and browse the messages which should work if the parent has reasonable technical abilities. You of course need test this well first.