Hungary issued this stamp in 1975 to commemorate the 100th anniversary of the Franz Listz Music Academy (Liszt Ferenc Zeneművészeti Egyetem). The stamp features a treble clef, an organ facade and an orchestra being led by a conductor.
One can view a virtual tour of the Great Hall here. From this tour one can learn that it is indeed the organ in the Great Hall that is featured on this stamp. I have not yet been able to determine who built this organ.
The academy's facility page mentions that reconstruction work has been taking place for the past two years, with scheduled completion in September 2011.
The organization, Friends of the Liszt Academy has this to say about the organs at the school:
The organ in the Bach-hall of the Old Academy of Music needs to be renovated urgently not only for the reason that it has been already used for fifteen years but because this is the only available organ for the Academy during the reconstruction period of the main building. The fundraising activity has already commenced for this special project.
The main organ of the Music Academy Main Building at Liszt tér has to be removed during the 2-year reconstruction time, and a new organ must be built. The financing of this huge project needs to get additional support.
The Organ Departments’ young and devoted professors envisaged an internationally active and attractive centre with other new small organs serving educational purposes. This long-term vision will need significant outside support as well.
So it seems there are two main instruments, but there are plans, it seems to replace the second of these two, which would seem to be that of the great hall.