On the new computer you need to download Hindenburg, install and activate with your registration email and registration key.
If you would like to have old sessions on the new computer, then move them to the new computer. You should remember to move both your session files and any associated audio files.
Now you can just go ahead and uninstall from the old computer.
Note that individual (personal) licences for Journalist only allows for installations on up to three devices at a time. So if you have already installed the program on three computers, please uninstall from your old computer and send us a note that you did so, in order for us to keep our system updated. Thanks.