where is the museum of this organization located?
Airport West Training Facility (formerly the TAA/Australian Airlines Flight Training Centre).
Trans Australia Airlines
Qantas currently allocates space at its Airport West Training Facility (formerly the TAA/Australian Airlines Flight Training Centre) for "The TAA Museum". 
who was lester brain? He was a pioneer Australian aviator and airline executive. where was he born? Forbes, New South Wales. did he take part in any war? Yes, World War II. what role did he play in it? He coordinated his airline's support for the Australian military. which airlines was he a part of? Trans Australia Airlines (TAA).
wiki:13608947
Trans Australia Airlines [SEP] TAA Museum
Qantas currently allocates space at its Airport West Training Facility (formerly the TAA/Australian Airlines Flight Training Centre) for "The TAA Museum". The museum displays artifacts from the life of TAA/Australian including service ware, uniforms, advertisements, and photographs and is open to the public during the week. The museum is immensely popular with former staff and the travelling public and is run by a dedicated group of volunteers.