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If the client’s WordPress site is running on an Amazon EC2 instance, then you don’t need to do anything. WordPress Core, Plugin, and Themes can be updated from the WordPress Admin Dashboard without having to do anything with the instance.
But if the client’s site was deployed using Amazon RDS and Elastic Beanstalk for high availability, then you will have to deploy WordPress on another instance of Elastic Beanstalk by first backing up your original WordPress site. The steps can be found at Deploying a High-Availability WordPress Website with an External Amazon RDS Database to Elastic Beanstalk
If you want to move to a new Instance of EC2 for some reason and set up WordPress on it, then I would recommend that you follow Digital Ocean’s Guide for Installing WordPress on Ubuntu 18.04 after you have created the EC2 instance and SSH-ed into it. You can find the guide for various other linux versions on that page as well.
If you want it to be in such a way that everything is automatically set up for you, then you should Launch WordPress with OpenLiteSpeed on AWS. The marketplace has the script build and will launch everything for you. You just need to point your domain name to the IP you get for the instance, open the site, follow WordPress 1 minute setup (First User Setup. You don’t have to add database information.), then export whatever you want. Updates to WordPress Core, Plugins, and Themes happen from the WordPress Admin Dashboard.