It’s possible, but not very likely.
By “captured”, in astronomical terms, we mean that the object did not form around the object it is currently orbiting. For the most part, this applies to moons of planets in our solar system that have a particularly unusual appearance or orbit.
We know that there are moons within our solar system which probably were captured by their planet. For instance, Mars has two moons (Phobos and Deimos) which are decidedly asteroid in appearance, and the prevailing theory suggests that Phobos and Deimos were formed elsewhere in the solar system and were captured by Mars later on. There’s also a moon of Neptune, Triton, which orbits the wrong way around its planet, which suggests that it was also captured after forming elsewhere.
In order for capture to work, two things have to happen: first, the smaller object has to pass fairly close to the larger object (the planet or star). The second is more critical - the small object also has to lose enough energy in the process of passing near the larger object that it can fall into an orbit, but not lose too much energy such that it simply falls into the planet or is otherwise destroyed.
Within a solar system, this isn’t completely unreasonable. Most objects are found within a thin rotating disk, and as objects interact with each other, they can gain or lose energy, and move further away from the sun or closer to the sun, which will let them pass near different planets. There are also a number of ways for the small moon objects to lose energy. For instance, a collision with a third object can slow it down, allowing it to fall into orbit.
Once you try and do this with a planet and a star, step one of this process becomes vanishingly improbable. The distances between stars are huge- so if you want your planet to be captured by a star that was not the star around which it formed, you have to throw your planet out of its system of origin (already a tricky thing to do) exactly in the right direction so it will eventually wind up passing near a star. And on top of that, once you manage to fling this planet miraculously in the right direction, the planet still has to lose energy, otherwise it will zoom right past the star and keep going.
There are so many planets and so many stars in the universe that this has probably happened a few times, but the odds are definitely not in favor.
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