In the early days of email, the internet service provider didn't want to be storing emails on their servers. They wanted you to log on, get your email, and then they would delete it. This is what Carlos is currently doing with Outlook. He's getting on the server, downloading the email, and deleting it from the server. It's an email protocol called POP. Carlos can continue to use POP if he wants, but in Outlook's settings he should change it to not delete the email from the server. That will leave the email on the server. This isn't the best way to do this, however.
The more modern email protocol is IMAP. This leaves the official copy of the email on the server. Unless you delete it from there, it will stay on the server. You can create folders, labels, etc on the server. Then the IMAP client will just read that information from the server and will even show the folders and labels you've created. This means that every message is available to every device, and changes made on one device will change them on your other devices as well. Google offers IMAP for free, but there are other companies like Fastmail that have this too.