I don't rely on cloud backups, so am not an expert on this, but it's hard to advise without knowing how the situation arose. What happened before he had to do what sounds like an account recovery procedure? What does "Google pretended that it didn't know him" mean? To me that sounds like they didn't recognise his email address, but the next bit sounds like a password recovery which means they did recognise the address. Has he done anything like a factory reset or a password change prior to this, or tried to free up space on his device (there are ways of doing that which will keep the backup with Google and there are ways which will delete it), or had any security issues with his account? Much as I don't trust any of these corporations, Google spontaneously losing his password and deleting many but not all of his photos is a low-probability event: not impossible, but I suspect that there's something on his side that's played a role, even if he doesn't know what. That's why knowing the background to this might help someone work out whether there is a solution.
The only practical suggestion I have is to check any "recycle bin" in the account for the missing images. If they are there then you can recover them, but it will probably be auto-deleted after some period so best to check soon.
But TBH it's likely that the only thing he can do is contact Google and ask them what happened to his data. Whether he even gets a reply I don't know - in reality even if they have screwed-up you have very little comeback on them (in fact it's probably buried in their T's and C's that you have none at all, though whether that would stand up in court is another matter).