I tried to fix it up before, but nearly broke my brains in trying to understand and map the situation. Exclaves within enclaves, that kind of thing. And different sources for the regions of UAE and Oman…
Administrative subunits of the U.A.E. are overlapping with Oman.
Edit: I’ve tried to fix it. It would be good to have accurate sources. I’ve compared our boundary with Natural Earth Data and GADM and the sources differ up to 2 kilometres.
I’ve found a map which tells that the area in the south belongs to Fujairah. According the German Wikipedia [1] and the map shown below the overlapping area is administered by both divisions.