For my own convenience I note the Wikipedia entry on moonrise and moonset, which describes something I had seen but had not observed (as Holmes remarked to Watson in “A Scandal in Bohemia”): the full moon always rises at sunset. The opposite is also true: the new moon (though you can’t see it) rises at dawn. And midway, the first quarter moon rises at midday and the last quarter moon rises in the middle of the night.
The Moon rises earlier each day, but it’s not regular: it can vary from half an hour to over an hour earlier (some of this depends on how close you are to the equator). This Astronomy magazine answer explains why.
Rise/Set Times with Moon Phases (YouTube) wonderfully explains moonrise and moonset and the phases of the Moon.