Hey Mal, thanks for your answer.
I eventually got the fire stick and precisely the same Amazon basics extractor that amir reviewed.
It is true that the fire stick connected to the Amazon basics extractor outputs Amazon music HD at 192khz no matter what, so it might not down-sample but it surely up-samples (the stick, not the extractor).
Anything else coming out of the fire stick/Amazon basics extractor is at 48khz. So I would say it (the fire stick) probably downsamples content when it is originally not 48khz.