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The term that describes the moon when it transitions from a full moon to the last quarter is "waning gibbous." During this phase, the visible portion of the moon is decreasing, and it is more than half illuminated but less than fully illuminated. This transition signifies that the moon is moving away from the full moon phase and approaching the last quarter phase, where only half of the moon is visible from Earth.

In contrast, the term "waxing gibbous" refers to the phase after the first quarter when the moon is more than half illuminated and is growing towards a full moon. A "new moon" indicates a phase where the moon is not visible from Earth, as it is positioned between the Earth and the sun. The "first quarter" refers to the moon phase that occurs before the waxing gibbous, where half of the moon is illuminated and is increasing towards a full moon.

Thus, the correct term for the phase between a full moon and the last quarter is accurately described as "waning gibbous," reflecting the moon's decreasing illumination.