Not sure if you have a question. If you want to know what it is just read the serial number plate on the side. It's a briggs and Stratton missing the flywheel, coil, gas tank, starter cup, engine shroud and possibly more.
I think the plate says model 6B, as for parts I'm guessing ebay will be where to look. You might be able to find a complete engine on market place or ebay. You could try a wanted add on this site. Looking at the condition of your motor you might want to consider a replacement but it does have a spark plug in it so it might look OK internally.
There is a puzzle in all this as my research showed they were made from 1943 to 1945. The pics of the fifties scooters while sharing some genetics are more stylizes than my scooter. Bremermanhas three and he also believes they are from the 40's. The flyer I had also said they were available with a 2 cycle engine. Haven't heard from Bremerman in a long while. I'd like to hear him weigh in on this. Also there were only 300 to 500 of the forties Scoots made.
As far as I could find was the engine was built in 1955, I assume the scooter had to be about the same time frame. Makes sense to me.
I was going to leave it they way it was with the original patina, but it doesn’t look like there is a lot of value in these so I may tear it completely down and have it powder coated and make it look new. Thoughts?