"My parents do not have a cat."
The tweet has since gone viral, being liked more than 479,000 times and has 76,000 retweets.
The post received thousands of comments, with many sharing their love for the cat and his father, while others poked fun at the heartwarming yet unexpected moment.
"You never own a cat, a cat owns or claims you - animals are very clever and this animal realised your dad needed some love," one person wrote.
"Travelling Therapy Cat reporting for duty," another said.
"You have the right to be comforted by a cat. If you do not have a cat, one will be provided for you, mysteriously and out of the blue, at no charge."
According to Falloon, the cat's name is Ziggy, and is understood to be from the neighbourhood.
Falloon's tweet picked up more likes than recent tweets from Donald Trump and Kim Kardashian.