When you change
email hosting providers for your account, do not edit the existing account and replace with your new email hosting provider. Chances are that you may lose all your existing emails. Instead
Copy all messages in the old account that you want to keep under “Local Folders”. POP account automatically copies all messages so in case you are using POP, you can ignore the step. For other applications, you can drag and drop any folders that are not available wherever you are copying them. Copy the contents of folders by using Control+A to select all the messages in the folder and then drag and drop the selected messages in one step or using Message-> “Copy to” and copy the content. Just recheck if all the messages are copied. Delete all messages in the old account, empty the trash bin, and compact the accounts folder.
For IMAP, there could be offline folders. Tools->Accounts settings-> Synchronization & Storage->” Keep messages for this account on this computer”. In case you want some files to work offline use File-> Offline for them to be visible.
Delete old account using Tools-> Account Settings-> Account Actions-> Remove Account.
Add new Account using Tools-> Account Settings-> Accou8nt Actions-> Add mail account.