360 727 converter question

Buying a newly rebuilt 727 and converter that was on a buddy's older Cuda (68) with a 340.

I researched but was fairly confused...but maybe I get what I need to do?

The 340 is most likely internally balanced, so the converter will be zero balance. I have read that some later 340's are externally balanced, however, the counter in that case would be done with the flexplate....both internal and external 340's would use same converter?

There is a B&M flexplate that will allow me to use the zero balance converter on my 360.

If I have this wrong, do not be shy. I tried my best to search and understand but this is so different from the old dark world of Chevy and Ford that I am from (and even then I know enough to only be dangerous)

Thanks!
No, the late '72 & '73 340s used an externally balanced convertor, ie weights welded onto the convertor itself FROM THE FACTORY. Aftermarket pieces will allow you to use a zero balance convertor and balance it via the flexplate on the later engines, but this is not how the factory did it; that's only in the aftermarket. '68- early '72 were internally balanced. As long as it's a neutral balance convertor, the B&M flexplate will allow you to run it on your 360. If it's an externally balanced 340 (different from the externally balanced 360) convertor, you'll have to source a neutral balance one to run with the B&M flexplate, or find a factory 360 727 (wieghted) convertor.
You need to figure out what you've got and then plan accordingly.
I know, clear as mud, eh?