You can leave the messages on the server and use IMAP to look at them from multiple devices in non-destructive ways.
If you must eventually move the mail out of the server then you can use IMAP devices in combination with one POP device that serves as the main mail archive, but only deletes the email from the server on a delay – say, 30 days. During those 30 days the IMAP clients continue to see the email and the POP client won’t re-download the ones it already has. After 30 days a message can only be found on the device that uses POP.