How to do

Method 01:

You can simply create an AWS data sync task for the particular work.

1. First Create Data sync task with source and destination location. Since you try to share data from AWS S3 to another S3 this task won't need any AWS agent.

2. Then RUN the task data will be migrate to destination S3 (Time will depend on the total size of data that you going to migrate)

Price:

1. In basic mode:

   

2. In enhance mode:

Method 02:

You can use Cross Region Replication (CRR) enable on S3.

These articles will guide you to how to replicate the existing S3 bucket. I think this method will be more cost-effective way for your task.
https://docs.aws.amazon.com/AmazonS3/latest/userguide/replication.html
https://aws.amazon.com/getting-started/hands-on/replicate-data-using-amazon-s3-replication/