In the impact, the rogue moon that hit the planet will cause a big scar. I am going to assume that such impact was caused eons before (intelligent) life wad formed on the planet. With enough time, the scar itself will heal and not leave any easily noticeable imprints of the event.
It will, for sure, deposit any loose matter that is on the surface of the planet. We're talking snooker on a celestial scale and even if the rogue moon/planet escapes, anything that is loose will be hurled forward by the momentum at the impact. Furthermore, with the impact both the planet and the celestial body will have large pieces torn off and while most of the pieces will be forming the new moon of the planet, some of them ought to fall down on it, too. I have not found any solid evidence that this is actually the case for our planet and moon, but some matter is inevitably transferred; exactly how much is, however, hard to tell. Even if a majority of the stones and dust misses the planet, some of it is bound to be captured by the gravity and it is bound to come falling down sooner or later.
If this is anywhere near how our moon may have formed, then it happened so long ago that the transferred magical rocks are deeply buried under ground. Although with the continental drift and other large scale events, pieces will finds it way to the surface.
You ask how they might agglomerate into crystals or rocks. An simplified explanation of the difference is that rocks are agglomerates of crystalgrains, meaning that small pieces of crystals are densely packed together while crystal are highly ordered molecular formations. A very common way to form rocks is by sedimentation, where looser material is packed densely by pressure from other matter which is deposited on top; if the dust and rocks from the moon are not able to form pure crystals, then this would be the most likely way that they eventually will make it into large pieces. In order for it form crystals, then it is required that the atoms it is composed of can form fairly periodic structures (although there are such things as quasicrystals, in which the atoms are ordered but not periodic). As author, you are of course free to choose whichever material you want as your lunar dust, it does not have to be the same as our lunar dust. As you used the word regolith - regolith is a term for any younger matter which has not yet formed sediments, it includes soil, gravel and other small pieces. If the rocks and dust from the moon is incorporated into the planet regolith at the time of impact, then that regolith can subsequently be packed into sedimentary rock and, thus, form larger rocks.
Yes, matter can very well be transferred from such event. Even if no matter were to be transferred, then there is still a possibility for rocks of the moon to make it down on the planet. Each day there are meteorites striking both Earth and the moon. Those hitting Earth are relatively harmless as our atmosphere protects us; for the moon, on the other hand, they have a chance to knock off pieces, which will be hurled into space. Such pieces will be orbiting Earth and the sun and will, eventually, fall down as lunar meteorites.