As this comes up in google search I'll post here:
In order to share desktop Opera information, pages, bookmarks, data or notes, you need to have My Flow enabled.
Simply opera://settings/?search=flow and use the slider to enable this feature, a small triangular right pointed arrow will appear on your side bar, and be an option on your URL settings now.
Once enabled, you can either use the taskbar button to send messages, paste in URLs or drop files, or click the new button on the URL bar to directly send the current page to your phone.
To use this feature on your Opera phone, simply tap the Opera Icon in the bottom right and select My Flow .