In Groove, users have the option to forward in individual messages to create conversations in your account.
To do this you will need to forward the message FROM the email address you have associated with your agent profile and send it TO the email address you're using for your mailbox in Groove.
Note: Do not forward messages to your @inbox.groovehq.com email address. This address is for auto-forwarding purposes only, not individual messages.
If you want to be able to forward in mail from multiple email addresses, you can add these other addresses as alternate emails in your Settings > My Settings > Profile.
When you forward an email from your agent address or alternate, Groove recognizes it's coming from you and strips your details from the message so that the conversation is created as if it came from the original sender.
Additional note: If you CC/BCC your Groove support email on a reply, instead of Forwarding directly into Groove, Groove will NOT recognize the you as the sender instead of the customer since the email reply is coming from you.