Nope, the trans-axle only looks like a F-Cub trans. Even the back plate is different. The Kohler K series engiines are great little work horses. Parts are not too hard to come by.
is a good source for parts dealers. You will recognize at least one of them.
First thing is that the Hydro fluid and filter usualy needs to be changed. A Hydroulic filter needs to be installed, not a "Oil" filter, they are different.
Refill the hydo with Hy-tran. It is designed for your Hydro.
Weak points..... the hydro linkage is usually wron and out of adjustment and "cobbled" repairs from previous owners. They are a solid machine.