Is it possible to backup from one e-mail account and restore to another?

I’m having a LOT of trouble with eM Client interacting with (Yahoo).  It constantly tells me it’s not connected to the server. Messages take forever to load. I’m thinking about switching to my Gmail account but want to take all of my email with me.  They’re all on Yahoo’s server.  About 2200 in the inbox, 1000 sent.  Via eM Client I could drag them into the Gmail folders but I’m afraid that would take forever and may crash. Help would be appreciated.

Hi Pat,
sadly, with this many emails, its bound to take a bit of time either way.
First please do a back up. Just to be sure.
I think that the safest way to move your messages will be to export them into EML files and then import them back in, but choose the gmail folders as the final destination.
Only then remove the mails from yahoo, if you wish.
This way you will have copies of your mail if anything goes wrong during the move.

Best regards,