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

Private Automatic Branch eXchange
PABX

    (PABX) A telephone exchange operated within
   an organisation, used for switching calls between internal
   lines and between internal and PSTN lines.  In contrast to a
   PMBX, a PABX can route calls without manual intervention,
   based entirely on the number dialed.  Not all PABXs can route
   external calls to internal numbers automatically however.

   (1998-08-07)