I have a player telling me he has sent me an invite to join his clan.

can't find any notice of that anywhere (email, player icon menu, wz mail...).

where should I look to find the invitation?

There will be a Join and Decline button for the invite on the clan page.

I thought WZ should send a notification and/or email about the invite, but that might be depending on your notification settings.

Check on https://www.warzone.com/notifications

seems it worked 🙃

Yes.