I can't see how SBRR could be transferable because the original owner of the business has to declare either that his business only uses one property or that
(a) non of his other properties has a rateable value above £2,899 ; AND
(b) the total rateable value of all his properties doesn't exceed £20,000 (or £28,000 in London).
When a new owner takes over the business premises, the local council has no way of knowing whether the declaration signed by the previous owner is still valid. (For example, a guy operating a takeaway business from just one shop might sell out to a firm that operates dozens of Burger King franchises across the region. The premises would then cease to qualify for SBRR).
So it seems apparent to me that a NEW application will have to be submitted in your case.