V.E.R.A. -- Virtual Entity of Relevant Acronyms (February 2016):

PBX
       Private Branch eXchange


The Free On-line Dictionary of Computing (30 December 2018):

Private Branch Exchange
PBX

    (PBX) A telephone exchange local to a
   particular organisation who use, rather than provide,
   telephone services.  The earliest PBXs were manual (Private
   Manual Branch EXchange, PMBX) but are now more likely to be
   automatic (Private Automatic Branch eXchange).

   (1997-06-25)