The importance of being earnest what leads Algernon to suspect that Ernest / Jack is a bunburyist

In play "The important of being Ernest" written by Oscar Wilde, Algernon is lead to suspects that Jack/Ernest is a bunburyist when he sees the inscription on Jack’s cigarette case from Cecily. Bunburyist is a coined word of Oscar Wilde that represents people who make up friends to avoid certain situations or persona to give them freedom to do what they want. Algernon has an imaginary friend Bunbury in country side which he visits when he wants to go away from London, so when he sees inscription he thinks that Ernest is Jack’s persona in London.