Cloning is not necessary—which is good because it will not create a bootable drive in Mojave.
Download the Mojave installer and install MacOS 10.14 on the new drive. After booting into it, you can use Migration Assistant to bring everything over (you will be prompted to do this).
If you want a minimum sized, Encore only, boot drive, bring all your network and System settings in Migration Assistant but cherrypick the applications and documents that you want to bring over. This will avoid privilege issues that can occur with copy and paste or sneakernet.
Once done, Encore should ask for your serial number and you should be good to go. If not, find the Encore Fonts on the old drive and copy them to the new desktop (Migration Assistant should have moved them over already)
. Double-click on them and then click on the Install button.