I've seen this here and there with and without the indefinite article.
I think it should be "happy birthday to wonderful you"
What's the correct one?
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Both versions are grammatical, whether they appear in greeting cards or not.
The customary birthday greeting in the United States is
You can also throw in a 'to phrase':
Happy birthday to you!
And this is the most repeated line of the Happy birthday song, which Wikipedia says Guinness Book of Records says is the "most recognized song in the English language."
You can modify you with an adjective, so you can say
Happy birthday to wonderful you.
Here you are saying that the person you are wishing happy birthday to is wonderful.
The song You, wonderful you also shows you modified by wonderful (YouTube)
Next, the version with the indefinite article is also possible:
Happy birthday to a wonderful you.
The use of the indefinite article with a proper noun or, in this case, a pronoun, can be used to mean 'one possible kind of you' or 'one type of you' or 'one version of you'. Here, the speaker is technically only wishing 'the version of you that is wonderful' a happy birthday. This does admit that other versions of you exist such as 'an angry you', a surly you', 'a greedy you', and even 'a dead you'–which would be speaking about a hypothetical 'dead you' if you were still alive, as in
The only you I want to see is a dead you.
The use of a wonderful you might seem more limiting than just wonderful you; this could be the case, since it is more realistic: you are not wonderful all the time, but you are wonderful part of the time. On the other hand, it can also be used to declare that a person (you) does indeed have 'a version that is wonderful'. Thus, its use in a greeting card, for example, allows the recipient (you) to revel in the fact that 'a wonderful version' of her exists, even though she knows that there are other "versions" or manifestations of herself that are not wonderful. Thus, there is some subtle psychology possibly going on in a wonderful you that is not there in wonderful you.
The use of the indefinite article before you is similar to the use of the indefinite article before a proper noun, as discussed in the question & answers about 'a screaming Dudley'.
I've seen a lot of answers and comments on ELL, especially about article usage, that say "it's a stylistic choice." But it is the difference in meaning, expressed by the grammar of a sentence, that provides the "stylistic" choices.