This name is a synonym of Mahonia bealei (Fortune) Pynaert.
The record derives from WCSP (in review)
(data supplied on 2012-03-23)
which reports it as a synonym with original publication details: Bot. Mag. 81: t. 4846 1855.
This name record (from WCSP (in review)) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Berberis bealei in version 1 of The Plant List.