I could have sworn I'd already posted a response to your question!
You can modify this mod:
https://vborg.vbsupport.ru/showthread.php?t=102338
In the XML file of that mod you will see:
Code:
<phpcode><![CDATA[if ($vbulletin->userinfo['usergroupid'] == 3)
If you change that "==3" to your registered user group (normally 2) then your registered users will only be able to send PMs to your mods and admins.