Is magnetic flux quantized inside a solenoid?

In some textbooks on quantum mechanics, the description of flux quantization in a superconductor ring based on the Aharonov-Bohm effect may lead some readers to a (wrong) conclusion that flux quantization occurs as well for a long solenoid with the same quantization condition in which the charge of cooper pair $2e$ is replaced by the charge of one electron $e$. It is shown how this confusion arises and how can one avoid it.