There are several services (S3, ..) where you can allow the client to pay for the call, and for the rest I believe that your account belongs only to you. What I do represents detailed billing, and I allow the company to recover costs.
You may need to migrate your environment. If your clients are not professional aws users, you might want to create a cloud-based script that allows them to run and access the environment in a few clicks.
G.
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