@Acer

Both "Happy" and "Belated" are adjectives, they are modifiers. A birthday is the anniversary of the date of a person’s birth, so it is always the same calendar date – it can’t be “belated”.

The phrase “Happy Birthday” is an expression of good wishes. The adjective “Happy” modifies the noun “Birthday”. When the expression “Happy Birthday” is given too late, then that expression is belated, but the birthday itself is not belated.

So you would say, “Belated Happy Birthday” because “Belated” modifies the entire expression “Happy Birthday”, while “Happy” only modifies “Birthday”.

Anyway, that’s how I see it.