Can my parents courier any medicine from India to USA with a valid Indian prescription and pharmacy bills?

Answer 1

Mostly you can only bring the medicines you use yourself.
So better phone the airline and ask if they are able.
If they are seen as drugs carriers it can be a hefty jail sentence.

Going to the USA you will also have to deal with the Immigration and customs in the USA, and again best phone before they start the journey.
In any case, they best declare the medicines on arrival, with the paperwork the customs people tell you they should bring.

I do not give you a good chance, as many medicines not available in the USA are on the forbidden list, and are seen as illegal drugs, on one line with cocaine and crack. With or without a prescription from an other country written for someone who is not traveling with them.

Answer 2

Yes, anybody can courier easily any medicine from India to USA with a valid Indian prescription and medical bills.

below Courier companies mostly accept the Medicine with 1. Doctor's prescription 2. Medical bill 3. ID proof xerox.

One Dunia International Courier http://www.onedunia.com/medicines-courier.html

Speedx Courier http://www.speedxcourier.com/medicine-services.php

International Courier Hyderabad Medicine Services http://internationalcourierhyderabad.com/medicine.html

Bharat Bandhan NRI Services http://www.bharatbandhan.com