I\'m using a service that puts the data I need on S3 and gives me a list of presigned URLs to download (http://.s3.amazonaws.com/?AWSAccessKeyID
=...&Signa
You can't do this with a signed url, but as has been mentioned, if you fetch and upload within EC2 in an appropriate region for the buckets in question, there's essentially no additional cost.
Also worth noting, both buckets do not have to be in the same account, but the aws key that you use to make the request have to have permission to put the target object and get the source object. Permissions can be granted across accounts... though in many cases, that's unlikely to be granted.
http://docs.aws.amazon.com/AmazonS3/latest/API/RESTObjectCOPY.html