All engines have the same bolt pattern...... Or will fit on any frame...... If you have the room under the hood yes it will fit...
Now are the shafts the same size ??? Yes in most cases... Your Briggs and Kohler are in the same class size, but measure them anyway.... 1 inch by 3 5/32 should be what you have........
The alternator is another factor if you have a electric PTO instead of a manual lever PTO...... Lets see what else is in store for you ?????? LOL...
The plug wire on the Briggs is a 6 pin and sometimes the kohler has the same thing also .......
Why do want to put a Kohler on your mower ???? If its a Courage Kohler then I have some tips for you to check before you put it on there ..
Let us know Mon Ami ~!~!