A verified document of an original certificate is a fairly common practise worldwide.
But be careful! Only a quality inspection, checking at site what is actually done with goods and tests (not only paper), will give you full verified certainity that you actually are receiving what you pay for.
There is a known historical example of a producer of high-quality plate material that did take all his plate material test pieces from the one and same plate. On top of it this plate was bought from a recognized high-quality competitor in another part of the world!
Another example is pipe-welding seams roentgenfilm, the same set af pictures reapeatedly sendt in 'as new set for new seams'. None roentgentest actually done!
On the other hand, your customers again will in their purchasing specifications, and you yourselves within your own commercial conditions and the local law, know what you risk and what is required.
If your supplier is well known, you could perhaps simplify. Maybe a verified statement from the suppliers QA department, required by your own QA- manager, which specifies the suppliers routine and tell how control procedure and control marking are done, and where the original certificates can be found (archive required!) will satisfy all parties.
I do not know of any law or code that says that all have to be original material certificate documents, but 'traceability' must be recognized for certain categories: pieces marked in such a way that certificates can be found/traced back to origin of the material.