@povilasp Since there isn't (or shouldn't be at least) any difference on how Chrome and Opera deal with cookies, then whatever configuration that works in Chrome should work in Opera.
The default setting for cookies doesn't work?
I forgot to mention in my original response that Chrome required this flag:
However, neither now nor the first time this thing happened this settings was fixing it for Opera.
Yes default settings for cookies doesn't work in Opera to enable third party cookies in this particular situation.