Thunderbird has no import from em client. But if your accounts in em client are imap accounts you do not need to import your mail, it will be downloaded from the server when you add your accounts.

According to [http://www.emclient.com/faq-em-client-features the eM Client FAQ], it can export mail as eml files and contacts as vCards. If setting up your accounts as IMAP does not recover all the mail, eml files can be brought into TB by simple drag and drop to Local Folders or by using [https://addons.mozilla.org/en-us/thunderbird/addon/importexporttools/ ImportExportTools]. To import multiple vCards, see [https://support.mozilla.org/en-US/questions/1158501 this post].