I am sure FBT is another English acronym used in Spanish. References for FBT are not very plentiful, but they're sufficient to link it to the meaning fixed-based trainer, which is a reasonably common term.

I think "session" would be better than "period", in the context of a training course.

"The FBT-Device has a full function cockpit enabling pilots and trainers to complete all required fixed base simulator training syllabus as set out by their chosen approved training program. "
http://www.jetflightsimulator.com/fbt-device

"Airbus 320 First Officer for major US airline. Former Boeing-757 Cockpit Procedures Trainer (CPT) and Fixed Base Trainer (FBT) Instructor."
http://www.linkedin.com/pub/johan-de-vicq/6/552/370

"AAA has a fleet of 35 aircraft, including Garmin 1000-equipped Cessna 172SPs through to Beechcraft Duchess for core training. It also has four training simulators, ranging from the Redbird FMX full motion simulator through to a recently purchased Boeing 737 fixed base trainer (FBT)."
http://www.asianaviation.com/articles/364/Pilot-Training

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Note added at 1 hr (2013-03-27 10:30:59 GMT)
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This document, from Mexico, illustrates how this acronym is used in Spanish:

"Además este entrenamiento deberá incluir módulos tales como.
Dispositivos de entrenamientos de vuelo FREEPLAY, CBT, etc
Simulador con base fija FBT
Simulador con movimiento completo FFT"
http://www.sct.gob.mx/fileadmin/DireccionesGrales/DGAC/03Vol...
Chapter 3, p. 18

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Note added at 6 hrs (2013-03-27 15:51:30 GMT)
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Just noticed an error in the answer line: fixed-BASE trainer, not fixed-BASED trainer.