It's quite a reduction in weight leaving all that paper behind! YMMV about the prescription - although a pharmacy might accept a photograph, the problem I have is border agents. If a customs officer is asking about my meds, then they already suspect something illegal, so I prefer to have that on paper I can hand to them. I have been questioned about a restricted medicine I was on - but once they saw the paper and confirmed the number of pills was a personal use amount, I was let through.
I haven't encountered that, so I wouldn't know. The border agents won't accept digital copies/pictures of the prescription? I guess for restricted medicine, it would be safer to bring paper as well.