The brisons used the Sachs parts, and the sachs engines looked very similar.
My guess is a sachs or some earlier variant as well.
EDIT
Sorry didn't see TKG's post above.
Yes - your pic is of a J&A Engineering engine - here's a link to their website.
http://www.j-aengineering.com/page26.html
If it's a Sachs jug and internals - it's basically the same as a Brison. to my knowledge Brison and BME are not related - Brison uses sachs parts, and BME uses a lot of Echo parts. Both make nice engines - I have a Brison 2.4 and it's a great motor.