i'm assuming your using IMAP
open edit --> preferences
select your account and press edit
goto defaults tab
change sent messages folder to: [Gmail]/sent mail
this will automatically add sent mail to your gmail account from now on.
just drag old sent mails onto this folder
Luri asked which would be best, POP or IMAP...
best is a matter of preference here. IMAP will treat all your gmail labels as seperate folders. Staying with pop, with all your sent and received mail in your inbox you could just create a filter locally. to create a filter goto: edit --> message filters. check its set to incoming. click add. for your sent mail: Sender, is, firstname.lastname@example.org, move to folder, destination folder. ok. Now goto your inbox press CTRL+A then CTRL+Y, this will apply the filter. play around a bit with filters for the rest of your email.