According to Official Guinness Records,
The fastest time to climb the height of Everest on an indoor climbing wall by a team is 4 hr 24 min 33 sec and was achieved by the Climbing Society at Texas A&M University-Commerce (USA) at the Morris Recreation Center at Texas A&M University-Commerce, Commerce, Texas, USA, on 18 January 2013.
The team managed to break this record whilst breaking another Guinness World Records title for 'Greatest vertical distance climbed on an artificial climbing wall in 6 hours (team)', climbing a height of 12,340 m (40,485.6 ft) in the six hours. The team of 12 climbers who broke both records was: Andrew Dahir, Hunter Joyce, Kathryn Cotsakis, Will Lian, Dustin Lux, Luke Raper, Deric Moore, Jake Gadberry, Rory Curtin, Dax Havrilak, Tyler King and Austin King.
For a complete list of 2013 records, please visit 2013 Guinness Records in United States.