If you can look for a good solution that transfer Thunderbird emails to Gmail then, I highly suggest the eSoftTools MBOX CONVERTER tool that supports MBOX form for 25 email clients, like - Thunderbird, AppleMail, OperaMail, Spicebird, PocoMail, Eudora, Gmail, etc. eSoftTools MBOX converter software gives a secure and comfortable surrounding for switching MBOX files into Outlook PST format. Get free demo editions of this tool which convert the first 25 items/folder as well into PST or various formats.
Read more:- Transfer Thunderbird emails to Gmail
Read more:- Transfer Thunderbird emails to Gmail