The first step will be to re-create all your existing email account through your DailyRazor control panel. So if you have email@example.com, firstname.lastname@example.org, email@example.com, etc. - you re-create them all.
After you do this, then you can go ahead and migrate your website over to our servers - Do not cancel your hosting account with your current host yet.
Next step now is to update your domain name's dns to point to name server address. DNS propagation will take 48 hours to complete globally. You can cancel your hosting account with your current hosting provider say after 96 hours of doing the dns change.
Now, your the existing emails you have at your current web host will not be transferred automatically. It will remain on their servers. So we suggest you download all of them using an email client like Outlook or Thunderbird - or any one of your choosing.
Given that dns propagation occurs at different times by different zones around the world - after you do your nameserver change you may notice some emails will go to your old server and some may come to our Server. This behavior is normal, but after dns propagation is complete, all mails will be coming to your new Server.