You really cannot hook them together, they are not interoperable all you are doing is powering parts of circuits and without much regard you will burn some of it up, blow some fuses….
You are way outside of plug and play.
You have a five wire rectifier, its missing a third yellow, so that is its own type.
Obviously there are lots of way to configure the electricals…
You may want to get a harness and rewire it to the new engine. You would need an AC R/R, CDI and Coil, good thing is that the engine you now have seems to be the most common type. The stator wiring on it is for AC and seems to use a common color code.