Thank you for the idea’s.
Most of them I already did.
I could see that emails are send but just not received.
Good news I found a solution for this problem. I installed Easy WP SMTP and it works now. The new website with woocomerce 3.4.4 sends out confirmation emails.
The other website with 3.4.3 has no problem with emails. That still works like always.
Thank you.