Click on Test and Cutover -> Launch cutover instance and confirm Launch in the popup.
This will trigger the cutover job (it will take ~10-15 minutes), you can find its details after clicking on Cutover Job ID in the Lifecycle section.
If you see Failed to launch cutover instances. One or more of the Source Servers included in API call are currently being processed by a Job error, this means that the test instance is still getting terminated. Check progress of that activity at Launch history page. Wait for the Terminate job to finish and then Launch cutover instance again.
Wait for the Launch status to change from Waiting to Launched / First boot: Started. At this stage your Webserver will be visible and Running in the EC2 Console.
Finalize the cutover
Click on Test and Cutover -> Finalize cutover, then confirm finalization of cutover to stop replication and cleanup resources used by Application Migration Service. Your migrated webserver of course will be still there in the EC2 Console!
The last step of migration is configuration of the application on migrated webserver.