Cassandra Austen (Jane Austen's sister) claims that Austen began writing Persuasion on August 8, 1815. There were two chapters that she concluded the book with that she wrote in July 1816, which she eventually revised and wrote three new chapters for by August 1816. Even though Austen had completed the manuscript for the novel, she hadn't taken any steps to get it published. In a letter to Austen's niece Fanny Knight from March of 1817 she mentions the novel, stating, "I have a something ready for Publication, which may perhaps appear about a twelvemonth hence. It is short, about the length of Catherine". Austen passed away on July 18th of that same year, and had left the rights to her unpublished novels to Cassandra. Henry and Cassandra Austen published the manuscripts in a four-volume set which included Northanger Abbey and Persuasion  on December 20th, 1817. Within this set was Henry Austen's "Biographical Notice of the Author" which finally revealed that Jane Austen had been the author of Sense and Sensibility, Pride and Prejudice, Mansfield Park, and Emma. 

“Persuasion.” Jane Austen Society of North America, Jane Austen Society of North America, https://jasna.org/austen/works/persuasion/.