I sent another test email, now using the insert image button, and it worked for me both in thunderbird and gmail's webmail.
So, seems this is the right way of embedding an image into email body, but for this to work one must upload the image to server and keep it there. If the image is deleted, the email doesn't show it anymore, as expected. The copy and paste method is easier and the image goes within the email, so it would be good if it worked this way too. But it isn't a major issue.
I had to upload the image by ftp, I'll try to make the connector working.
Thanks for your help.