> The Mycenaean palaces had developed a syllabic script, which we call Linear B, to represent their spoken Greek. This form of writing is entirely lost. In the 8th century, the Greeks will adopt an entirely new script – borrowing the one the Phoenicians are using – to represent their language

You've misread something. Linear B encoded Greek, but is not related to the Phoenician-based script.

The Greeks lost writing as a technology during the collapse, so the two alphabets aren't related. They just represent the same language.