No, there isn't a way to direct S3 to fetch a resource, on your behalf, from a non-S3 URL and save it in a bucket.
The only "fetch"-like operation S3 supports is the PUT/COPY operation, where S3 supports fetching an object from one bucket and storing it in another bucket (or the same bucket), even across regions, even across accounts, as long as you have a user with sufficient permission for the necessary operations on both ends of the transaction. In that one case, S3 handles all the data transfer, internally.
Otherwise, the only way to take a remote object and store it in S3 is to download the resource and then upload it to S3 -- however, there's nothing preventing you from doing both things at the same time.
To do that, you'll need to write some code, using presumably either asynchronous I/O or threads, so that you can simultaneously be receiving a stream of downloaded data and uploading it, probably in symmetric chunks, using S3's Multipart Upload capability, which allows you to write individual chunks (minimum 5MB each) which, with a final request, S3 will validate and consolidate into a single object of up to 5TB. Multipart upload supports parallel upload of chunks, and allows your code to retry any failed chunks without restarting the whole job, since the individual chunks don't have to be uploaded or received by S3 in linear order.
If the origin supports HTTP range requests, you wouldn't necessarily even need to receive a "stream," you could discover the size of the object and then GET
chunks by range and multipart-upload them. Do this operation with threads or asynch I/O handling multiple ranges in parallel, and you will likely be able to copy an entire object faster than you can download it in a single monolithic download, depending on the factors limiting your download speed.
I've achieved aggregate speeds in the range of 45 to 75 Mbits/sec while uploading multi-gigabyte files into S3 from outside of AWS using this technique.
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