How can I switch between stores in Shopify Inbox quickly?

I quit using it because of this issue. We have 6 sites. Unless something has changed, you only receive message notifications for the store you’re logged into. What if a customer messages you from another store? You need to be able to receive notifications for all your inboxes. I would also suggest a Slack integration (or similar) and allow you to assign each inbox to a channel in Slack.