Wix has a filter look up site that lists many equivalents. wixfilters.com
The Wix filter for the Kohler 12-050-01 is a 51056.
KOHLER 1205001
The Fram equivalent of the Kohler 1205001 oil filter is the Fram PH3614. Both filters are designed for similar applications and provide comparable filtration performance, ensuring engine protection in compatible engines. Always verify compatibility with your specific equipment before making a purchase.
Baldwin - B10140 Fram - PH8172 Kohler - 1205001 B&S - 492932
Fram makes a poor quality filter which I advise you to not buy. Purolator on the other hand makes an excellent high quality filter which costs no more than a Fram. Your Kohler filter 1205001 cross references to a Purolator L35310 sold at Advance Auto Parts and some Walmart stores. I recommend you use only synthetic oil in any air cooled engine.
12-050-01 may be a better number to search oil filter suppliers for a substitute. The Kohler oil filter 12-050-01 was superceeded to 12 050 01-S1. Fram still has the old number and it crosses to Fram filter PH8172
Equivalent to 052-050-02
That would be a Fram PH8172
PH3614
PH4967. Fram specifically says the Kohler 7.3E uses this filter
sfwe
That is a NAPA 1348.
I use Hastings filters. The Hasting replacement is a LF157.