"Belated happy birthday" or "happy belated birthday"?
Personally, I've used both versions. Nevertheless:
- Belated birthday is nonsense, since the anniversary is the anniversary, and cannot be postponed even if the celebrations are.
- Belated happy birthday, strictly, is also nonsense because the birthday has already gone and may or may not have been happy.
Therefore I would suggest something along the lines of:
- Belated birthday wishes (as suggested in another answer)
- Hope you had a Happy Birthday. Sorry I missed it / Sorry I'm late.
Well belated means behind date or late.
From Oxford English Dictionary:
belated, adj.
- Detained beyond the usual time, coming or staying too late; out of date, behind date.
So, if you're wishing someone a Happy Birthday which is late, you would use:
Belated Happy Birthday
"Belated", of course, refers to something that has been delayed. From Merriam-Webster:
be·lat·ed adjective \bi-ˈlā-təd, bē-\ 1: delayed beyond the usual time 2: existing or appearing past the normal or proper time
So, to wish someone after their actual birthday, the best phrase in my opinion would be "Belated birthday wishes", because it's just your wishes that got delayed.
Among the two options yo've given, "Belated Happy Birthday" is more common in my part of the world than the other.