Credited to Nepal. Papermaking itself reached Nepal from China through Tibet, and Daphne fiber paper is also part of Tibetan practice. Nepal's claim is to the lokta tradition as developed and kept up in its own hills.
How it began
Papermaking was likely introduced to Tibet from China as early as 650 CE and reached Nepal through Tibet. Some of the earliest examples of paper made from Daphne fibers date to the 9th century, and paper was being produced through Nepal by the 12th century. The use of Daphne, along with Edgeworthia and the roots of Stellera chamaejasme, is described as largely unique to Tibetan and Nepalese papermaking.
How it works
The bark of the Daphne shrub is removed and the softer inner bark, the phloem, is separated. It is cut into strips, soaked and rinsed, cooked with lye and beaten to separate the fibers. The fibers are floated in water over a traditional paper mold and left to dry on it. Daphne grows only above a certain altitude, which makes it abundant in the mountain areas of Nepal.
What lasted
The plants used are mildly toxic to people and animals, and paper made from them acts as a natural insect repellent. This delays insect damage and decay without climate control or later preservation treatment, which greatly prolongs the life of the paper. Wikipedia notes that the earliest surviving lokta paper document is kept in Nepal's National Archives.
Where it stands today
When Dorothy Field collected samples in the mid 1980s, fine paper mills in Nepal were dying out because few people wanted or could afford the handmade product. Since the 1980s the government of Nepal has put money into reviving the tradition, and lokta paper is increasingly sold outside Nepal as a luxury product.