A private activity is usually created from an imported email, when users forward the email from the client to each other and always paste the email assistant's address into the copy. Another reason could be not forwarding the incoming email as an attachment.
For the email to be included in the correct client in RAYNET, forward it to the CRM only at the end, when you’ve already agreed it with your colleagues. Send the email with its entire history as an attachment to the email assistant's address.
Tip at the end :)
Try using Discussion rather than forwarding emails to each other. Forward the email from the client to CRM and then just discuss . You will have everything in RAYNET and with the right context ;)