The Shakespeare Fellowship was the name used by an organization, founded in 1921, devoted to the Shakespeare authorship question. Originally it sought to represent all alternatives to the authorship of William Shakespeare, but it later became strongly identified with Oxfordian theory: promoting Edward de Vere, 17th Earl of Oxford as the true author of the works of Shakespeare. The original organisation is now known as the "The Shakespearean Authorship Trust".
A second organisation dedicated to the aims of the original Shakespeare Fellowship was founded under the name in 2001. In 2013 it merged with the Shakespeare Oxford Society to become the "Shakespeare Oxford Fellowship".
More information on the Wikipedia page [1]