I believe Singapore Airlines had Learjets to train pilots, at least some time in the past. Also remember PanAm in 1968 had thought of using DA-20 Falcons to do the same thing, but never came to be a fact. So did United, I saw pictures of a Falcon 20 with PanAm colors, and a Learjet 23 in United markings...
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Learjet (particularly old 20 series) are excellent "jet trainers" and all new hires I have seen with that aircraft background do a good job in airline training environment. These old Lears are not easy planes to handle, and can kill you if you dont watch-out...
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The CEO of "an airline that I know well" has the use of a Learjet 31A, but that is just to enjoy nice company while flying to exclusive resorts... I dont think he likes the service in F class of his own airline, or the schedules... Good excuses...
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Happy contrails