Here is what Opera wrote about old browsers:

"...If you can not upgrade to the new browser or do not wish to, your local data will remain on your machine but will not update on the Opera Link server. We recommend that you migrate your bookmarks, so you can still access them through our new service's web interface. You can find the migration tool at sync.opera.com/web/."
http://r.mails.opera.com/m0sk95qdu9nf.html

So bookmarks which are on an old browser, should be available using the new service's web interface - if I understand them right. But my Opera Mini (java on my old phone) does not allow to synchronize this way - or at least, I don't see how, even though I'm logged into my account.

But Opera announced this "sweet tool" for modern Opera browsers, and obviously for the time after Opera link has been closed. The announcement is still visible here:

http://webcache.googleusercontent.com/search?q=cache:IYhQUsWqiCEJ:www.opera.com/ro/link+&cd=1&hl=de&ct=clnk&gl=dk

Hello - where is this "sweet tool" to migrate Opera Link bookmarks, which Opera announced before they closed Opera link? (se below, last sentence)

http://www.opera.com/link
Opera Link

Opera Link will close in December 2015. At that time, you will no longer be able to synchronize your browsing data using the Opera Link service. Also, you will no longer be able to access your data through the Opera Link web interface.

But, don't worry. Our new generation of Opera browsers allows you to sync bookmarks, Speed Dials, open tabs, browsing history, settings, passwords and more through our new synchronization service baked right into the browser. We even built a sweet tool for you to migrate your Opera Link bookmarks.