Comments moderation

Log in with your admin account and go to wp-admin > Settings > Discussions and uncheck the “E-mail me whenever” checkboxes.

Sorry I don’t think that will work. The email notification is sent to the e-mail address listed in the wp-admin > Settings > General Screen. Replace your e-mail address by that of your client.

replacing the emailadress is no option, because than my gravitar (connected to the mailadress) will change as well.

I know it’s not the WP fix you’re looking for but if the only issue remaining is you getting unwanted emails, you could just block those from your email client.

Maybe this plugin: https://www.ads-software.com/extend/plugins/email-alerts/

@keesiemeijer: looks like that is infact what I was looking for! Installed this and activated it, so now I have to wait to see if it works. Let you know later.