No easy answer...
When you login on the desktop all mail is downloaded to that computer, when you login on the laptop all mail is downloaded there.
There are mail applications that leave the mail on the server but this can cause problems with account sizes.
Also briefcase applications that allow settings and files to be the same on each system. do a search
I notced this is an irritation on occasions so setup another e-mail account for my own use and when on desktop send stuff I want to keep there and then download on the laptop and vise-versa.
dont forget which sent it or you get it twice.