Just post the pics here - we will soon sort them out. !
We have quite a good record for even oddball bikes, although sometimes it takes a little while.
BSA were one of the biggest manufacturers back then, so they are VERY well documented.
They also had quite a range of models then, so you sometimes need a little inside knowledge to read the brochure fine print - to distinguish some seemingly very similar models.
If the frames are visually identical (?) it might be quite difficult to sort which one the engines belongs to, in the absence of factory records or a previous rego document for that particular bike.
Is there something broken or damaged on one frame, thats often the reason for another one being involved. (?).