After moving Thunderbird folder i.e. ~/.thunderbird to another computer, it could not find the mailbox of the profile. It created a new profile. This was due to the change in the path where ~/.thunderbird folder was restored.
To overcome this issue, open a terminal window and enter the following:
cd ~/thunderbird <enter>
./thunderbird -profilemanager <enter>
and select the profile to open. This will then open the mailbox.