d/l Gmail occassionally on iphone 5s but still want to get it in Mail on MB Pro

[Christopher11]

Hi there. I just upgraded to iPhone 5s. On my iphone 4, which had iOS6, I could download mail to the Mail inbox on that iPhone and still get it on my MB Pro later. It's convenient. however, I did so today on the iphone 5s, and now Mail on my laptop thinks there's no new mail Gmail messages to fetch. I hope I explained that well enough. Is there a way to set Mail on my iPhone to download, but just as a duplicate, not as my primary?

Thanks so much for any response, really appreciate it.

 

[C DM]

How do you have your Gmail account set up on the phone (and on the computer)?