How to implement S3 replication for existing objects in CDK?

1. I already can replicate existing objects from aws console by setting up a batch job.

2. But how to do the same thing in CDK?

3. Currently, in CDK, I can only implement live replication for a new created bucket, not for existing objects. Here is

// create a new bucket and add replication rule 
// How to do replication for an existed bucket? 
const source = new cdk.aws_s3.CfnBucket(this, "SourceBucketNew", {
      bucketName: `replication-source-bucket-${this.account}`,
      versioningConfiguration: {
        status: "Enabled",
      },
      replicationConfiguration: {
        role: role.roleArn,
        rules: [
          {
            destination: {
              bucket: dest.bucketArn,
            },
            status: "Enabled",
          },
        ],
      },
    });