No, Galileo did not use a telescope to observe the phases of Jupiter. He did, however, use a telescope to observe the phases of Venus.

The phases of Venus are similar to those of the Moon, and Galileo's observations of them provided strong evidence for the heliocentric model of the solar system, where the planets orbit the Sun.

Galileo did observe Jupiter with his telescope and made groundbreaking discoveries about the planet's four largest moons, now known as the Galilean moons.