scurrell said:You need to have them set as IMAP accounts on both devices.
twerppoet said:It's a bit of a pain, and I've never done it, but GMail can be set up to send and get email from a POP account. Of course, if this feature breaks you may never know you've missed something, so you still have to keep an eye on the original account.
Centralize mail from different accounts - Gmail Help
Sending mail from a different address - Gmail Help
While I don't recommend it for a permanent solution, it can certainly be used while transitioning to the more flexible GMail account.