Install Steinberg Download Assistant, run it and log in. That will update (or install for the first time) Steinberg Activation Manager, Steinberg Library Manager and eLicenser Control Center.
Buy the upgrade you need.
Enter the Download Access Code into Steinberg Download Assistant on the computer that has the Dorico 3.5 eLicenser. That will add the temporary Dorico 4 licence to your My Steinberg account and walk you through the eLicenser process to turn your Dorico 4 licence into a perpetual licence.
Use Steinberg Download Assistant to install Dorico 4 on your computer.
You might have to sign in to Steinberg Activation Manager to activate Dorico 4 before it will run.
On your other computer, all you have to do is install Steinberg Download Assistant, use SDA to install Dorico 4 then, if prompted, sign in Steinberg Activation Manager.