@aral I contacted hostpapa by chat. This was the response (by e-mail)
Hi,

I have checked with the client. They have confirmed that their forum clients can not send emails outside their forum. And this issue is not directly linked to their account as the users in the spam evidence you have provided are merely using their domain name but not actually from their domain.

Please let us know if you have any questions.

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With best regards,

Pradip Majumder

Systems Administrator
HostPapa Inc.