Festerthecat

According to The Story of Fester Cat, a book mostly written by Fester Cat, (PROSE: Fester and the Christmas Mouse) he had a Facebook account set up sometime in 2007. Fester used the account to see the people of the wider world and their adventures, and Paul and Jeremy helped Fester post updates about his life. (PROSE: The Story of Fester Cat)

Behind the scenes
In the real world, Fester's account was set up in 2012, not 2007, however this discrepancy is easy to explain as Fester is an. Additionally, the full name of the account was not mentioned in The Story of Fester Cat.