The ISS orbits at about 400km. The distance to the moon is about 385,000km. From the moon, and especially the sun, the Earth and ISS are basically in the same place, so the phase of the moon doesn't appreciably change in low earth orbit.

A werewolf on Europa (and others) could be in a full moon much more often. Even on the side facing away from the sun, it may still have plenty of light due to the reflection from Jupiter.

Maybe they would have to hide away from society once per month whenever they turn into a human monster?

I think they would suffocate and freeze the same as anyone else 🤷‍♂️

Well, I'm not going to pretend stuff's not going to get real weird for a werewolf, but I can clarify some of the orbital mechanics a bit.

First of all, the moon still has all its normal phases from orbit and in pretty much the same durations. For the moon to always be full, you would have to be permanently between the sun and the moon, which is not where an orbit will typically put you. A couple ways you could do this: You could orbit the sun instead, or at least orbit closer to it than Earth does. From Venus's orbit, both Earth and our Moon are always "full". Or you could set yourself up at a lagrange point between the Earth and the Sun.

The other less simple way you could achieve an always-full or at least frequently-full moon is to get into what's known as sun-synchronous orbit.

The simplest way though, might be to just land on the Moon's surface. The terminator between day and night on the moon's surface only moves at about 9.6 miles per hour, even slower the closer you get to the poles. An athletic werewolf could probably jog to keep up, and stay permanently on the "full" day side.

Same thing that happens to everything else.

If the transformation is because of the light from the moon there are a few changes we could expect. First, the cycle would still be matched to the lunar cycle of about 28 days just like on earth as that cycle is driven by the relative positions of the moon, sun, and earth. If the moon is further away from the sun than earth it is lit up more, most at opposition to the earth. In contrast the brightness would go down as it enters alignment between the sun and earth, peaking with a new moon.

Second, the near lack of atmosphere would likely increase the number of days which would be sufficient to trigger the transformation. Maybe it would be 5 nights instead of 3 nights, or maybe the transformation would be more intense leading to more extreme features or even new traits.

As for another planet and moon system, earth is unique here. No other moon is as close in size to the planet it orbits with the exclusion of dwarf planets Pluto and Charon. The bulk of moons are way smaller and also orbit around planets way further away from the sun and so would be far less bright. Perhaps not enough light would be reflected for there to be any transformation, while a confluence of moons may work together to have a higher impact on occasion.

In a more science fiction setting I would imagine having reflected light cause the transformation could make things like a ring world, a spinning ring with a central reflector, interesting. The starlight reflecting off the mirrors would theoretically make the whole ring be constantly lit for wearwolves and make night, changing the mirrors to reflect no light, the only time without wearwolves.