Export AWS Managed Apache Flink savepoints to S3

We'd like to migrate from AWS Managed Apache Flink to our self-hosted Flink cluster on EKS. As part of this, we need to migrate Flink operator states to the new cluster.

From my understanding this can be done by creating a Flink savepoint and start the new Flink job from this savepoint. However, we don't find the options to create and download Flink savepoint in AWS Managed Apache Flink Console or API. It's possible to create and recover from snapshots but it seems that we can't download or export the snapshots to S3.

My question is how we can download/export Flink snapshots or savepoints to S3 in order to do the migration? Thank you!