Mr Stilwell's parents were still deciding whether to fly to New Zealand from the UK, but Mr Thomas said he had emailed them photos of their son in hospital.
He said Mr Stilwell did not remember anything from the incident, but was amused to see it being reported around the world.
The Auckland Transport worker broke bones in his back and neck, and has suspected internal injuries.
Mr Stilwell, who is from Brighton, was on a night out with fellow travellers when he became separated from them and went home to the Volt apartment complex.
He couldn't get into his locked unit, so he woke a neighbour about 2am on Sunday and asked her if he could lower himself down from her top 15th-floor balcony to his own, directly underneath.
Geraldine Bautista, 28, said Mr Stilwell slipped from her grasp and plummeted onto a building about 13 floors below.