For example, suppose your first account username is firstname.lastname@example.org and second is email@example.com.
#s3cmd –configure : Configure for acc1 aws account
and create similar bucket (not same bucket name) in the acc2 account and set those bucket permissions to (Gurantee=)Everyone – (Tick)Upload/Delete.
Then you can use s3cmd (using the credentials of the acc1) to do something like:
s3cmd cp s3://acc1_bucket/folder/ s3://acc2_bucket/folder -r
All transfer will be done on Amazon’s side.