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 visibile as subfolder 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.
First you need to download MboxImport from here
Install MboxImport in Thunderbird
In Thunderbird, go in “Tools” –> “Extensions” and click on “Install”;
pick the xpi file you downloaded and follow the instructions;
To export, it’s sufficient a right-click on the folder or on the account and to choose the voice you want from the menu “Import/export”.
Once you have saved all the folders/files into the Mbox format, just go into Evolution and select “Import” and follow the wizard using “a single file import” and select your xxxx.mbox file and then select which folder in Evolution you want to import into.
For importing the address book from Thunderbird to Evolution, use T-birds address book export function and save the address book as a .csv file.After finishing address book check everything is fine or not.