Kernan succeded Henry around 1896. I have two G. Henry & Co. and 4 Kernan Mfg. Co. catalogues. All of the Kernam catalogues mention that they were the successors to G. Henry & Co. One of them is dated 1898 on the cover. One says Incorporated in 1897 and one says "Not Inc.".

A good way to trace the timing would be through Chicago Business Directories which the Chicago Public Library could help you with.

Hope this helps.