Small Engines (Lawn Mowers, etc.): replace B & S with Kohler engine, k series, last decade

Question
do you know or have idea what kohler engine will replace this b&s engine model# 446777, type#0126 E1, CODE#050609YG

Answer
I do not have Kohler to Briggs engine cross reference.  The old K series Kohler were outstanding engines but over the last decade Kohler quality has not been as good as it once was.

We have stopped carrying Kohler parts due to this reason.

Is there a reason you want to switch engines from Briggs to Kohler?
Let me know.
Eric