Who is the author of Orpheus and Eurydice?

As the other answer said, the Orpheus and Eurydice myth has no first author. Nevertheless, a modern writer, Hugh Lupton, retold the story in a book for middle schoolers published in 2013. His book is called Orpheus and Eurydice.
In it, he retells the classic story. While details and versions of the story change from author to author, Lupton tells the following version:
Orpheus is an extraordinary musician. His music enchants the world. He falls in love with and marries Eurydice. Sadly, however, she is bitten by a poisonous snake and dies soon after the wedding. Orpheus is so grief stricken that he goes down to the underworld to retrieve his bride. He plays his music so beautifully that the ruling god and goddess of the underworld, Hades and Persephone, allow Orpheus to leave with Eurydice. They establish one rule, however: he must not look at her until they are back on earth. Naturally, Orpheus looks at his wife. More happens, but I will leave you to read the story.

The legend of Orpheus and Eurydice is one of the most well known of the Greek myths. Many people have written it down and added their own elements to it over the years, but by and large, it is considered part of an oral tradition from the Ancient Greek world, one of many stories the Greeks told about their gods.
Of course, part of the reason it survives to us today is because it was written down by Greek authors thousands of years ago. Virgil wrote the story down, as did Ovid and Plato. But all of these authors were simply using a story they already knew—and which their audience would also have already known—in order to make their own distinct points about humanity, sin, and how we interact with the gods. None of them made the story up. The idea of authorship therefore doesn't really apply to a story which seems to have been the product of communal worship of a pantheon of gods, thousands of years ago.