Full-Text Search against serial numbers?
Full-Text Search would be able to efficiently Search for a word with a prefix (Prefix Term) or Search for a specific word or phrase (Simple Term), but not a suffix as you described. You can achieve what you need using LIKE.

As you can see in Eugene Elutin's answer for a Using Full-Text Search thread:


  partial and suffix match in T-SQL can be only done using LIKE, which
  will do full table scan to find relevant rows.


Here's one way of doing the search you described


  Full-text search only supports prefix search. In some circumstances,
  reversing the string, indexing that, and then searching for the
  reverse of the suffix can be made to work reasonably well.
  Fundamentally, though, FTS is not designed for the purpose you
  require.


But that approach would fail to find this other serial KN5672281 when trying to search for 7228.