Go to Services, Database Migration Services. Then, click on Database migration tasks. After, click on Create task.
In Task configuration, use:
All other settings can be used as the default values.
On Table mappings, select Guided UI. Expand Selection rules and click on Add new selection rule
The rule determines what will be replicated. In Selection Rules, use the settings (Note that % symbol means ALL):
Then, click on Create task.
Now, your replication from the EC2 database instance to Aurora Postgres is running and the data started to be replicated.