To move a conversation to another mailbox, click the more menu in the top right of the page. Select the "Change inbox" option and then select the mailbox where you want to move the conversation.
A user can only move conversations to mailboxes they have permission to see. If you want your team to be able to move conversations to inaccessible mailboxes, you will need to contact us at support@groovehq.com to enable this special preference for your account.