As stated by joyful noise, the pvc float is the preferred float replacement for concrete fill pots, much more user/installer friendly than the brass old style flip-n-float your holding in your pic, but those work to, at least the ones i buy from my pool parts wholesaler do, and what your holding looks just like one, the style you hold in pic can be frustrating for a first timers attempt at replacing it inside the pot, to the point of cross threading it, and damaging the threads on the pot, when trying to install the brass float it can feel awkward when trying to thread it in due to the float, linkage, etc, the fact you said it was missing to begin with somewhat indicates the previous owner had damaged the fill pot fitting, making you think it is a thread cut related issue, when it is not. they are the same style concrete fill pots that have been used for a long time, i have a tap, that if needed, can clean the fill pots damaged threads, you wont believe some of the things ive seen, that people have butchered, destroyed, or improperly installed, etc.
Generally speaking the float wont just thread on, you have to start it a turn or two by hand, then as it gets hard to turn by hand, tighten it with a pair of channel locks, a little more to orientate it, and seat it better in the pot. your not going to be threading this thing in more than a few turns no matter what. Examine the fitting on the concrete pot, the plastic pvc float assembly is the best bet though, as it being plastic, may help it to overcome any imperfection on the pot threads.
everything being normal, the float you have in your pic should work, they were commonly used for many years in fill pots, until the pvc float came along. that red washer is not used, and that nut should back off to (i could be wrong about the nut, its been awhile since i used that style float)
