When setting up your e-mail account on a second computer / laptop / other device, we recommend using the IMAP account type on all of the devices to ensure that your emails sync correctly over all the devices.

If you prefer using POP3, then please remember to do this:

You need to make sure a copy is left on the server, under your e-mail account settings --> more settings --> advanced, you need to tick the box that says leave a copy of e-mail messages on the server. If this is not ticked, you will not receive all your e-mails on all the computers / other devices where it is set up on.