well I've had the same problem and I'm still struggling with it.... come on that is none even none of the helpers from Opera Ltd who would provide a solution from for that I mean

...
I cannot find (in Ubuntu Linux on my phone attached via USB) any kind of folder which would indicate that it belonged to Opera Browser I have some dozens and dozens / almost 200 / saved pages and so on and I would like to transmit it to my new S 5....?!?

I cannot either locate my saved websites in opera mobile.... there is some great stuff like the advice to get along with the angels before the ten commandments aura inside behind politics or uhm reading scriptures to telling the truth about our world and beyond (A collection of formerly "hidden" manucripts....) I sent some bug report to 'opera help', yet no one replied ... before upgrading android I would love to backup these pages or copy the websites to pc for printing, but no one wants to know either part of the truths anyway ... nor help nor would Love to hear them .. i know now. Good luck anyway