If you want to Import your mails from Evolution to Thunderbird there is very nice utility called MboxImport .
Thunderbird, like many other email clients, uses the mbox format to archive the emails.It's curious that Thundebird has not a function that let you import or export files in this format and this lack is sometimes a problem when you want to move the accounts from a pc to another one or when you want to migrate (for example) from Mozilla to Thunderbird.Anyway this kind of import can be made very easily copying the mbox file into the directory "Local Folders" (it is inside the profile directory) with Thunderbird close; restarting the program, the mbox file will be visible as sub folder of Local Folders.To export, you must just copy the email files that are inside the account's folder.This method can give some troubles, above all for people not very expert with Thunderbird, because the profile's files are into a hidden directory, whose path changes with the operative systems or also with personal needs.